WO2005092071A2 - Procede et systeme de telemetrie de photons enchevetres - Google Patents

Procede et systeme de telemetrie de photons enchevetres Download PDF

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Publication number
WO2005092071A2
WO2005092071A2 PCT/US2005/009853 US2005009853W WO2005092071A2 WO 2005092071 A2 WO2005092071 A2 WO 2005092071A2 US 2005009853 W US2005009853 W US 2005009853W WO 2005092071 A2 WO2005092071 A2 WO 2005092071A2
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Prior art keywords
photon
photons
cavity
distance
entangled
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PCT/US2005/009853
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English (en)
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WO2005092071A3 (fr
Inventor
Thomas Zaugg
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General Dynamic Advanced Information Systems, Inc.
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Priority claimed from US10/850,394 external-priority patent/US7609382B2/en
Application filed by General Dynamic Advanced Information Systems, Inc. filed Critical General Dynamic Advanced Information Systems, Inc.
Publication of WO2005092071A2 publication Critical patent/WO2005092071A2/fr
Publication of WO2005092071A3 publication Critical patent/WO2005092071A3/fr

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Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S17/00—Systems using the reflection or reradiation of electromagnetic waves other than radio waves, e.g. lidar systems
    • G01S17/02—Systems using the reflection of electromagnetic waves other than radio waves
    • G01S17/06—Systems determining position data of a target
    • G01S17/08—Systems determining position data of a target for measuring distance only
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C3/00—Measuring distances in line of sight; Optical rangefinders
    • G01C3/02—Details
    • G01C3/06—Use of electric means to obtain final indication
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/48—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00
    • G01S7/481—Constructional features, e.g. arrangements of optical elements
    • G01S7/4818—Constructional features, e.g. arrangements of optical elements using optical fibres
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/48—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00
    • G01S7/491—Details of non-pulse systems
    • G01S7/493—Extracting wanted echo signals

Definitions

  • the invention relates to deteiminmg distances.
  • the invention relates to using one photon of a pair of entangled photons, reflected off an object, to determine a distance to that object.
  • Photons are quanta of electromagnetic energy. Multiple photons may be entangled or not entangled. Photons that are not entangled together (i.e., random photons) exist as independent entities. In contrast, entangled photons have a connection between their respective properties.
  • entangled-photon pair Two photons entangled together are referred to as an entangled-photon pair (also, "biphotons").
  • photons comprising an entangled-photon pair are called “signal” and “idler” photons.
  • Signal photons comprising an entangled-photon pair
  • idle photons.
  • Measuring properties of one photon of an entangled-photon pair determines results of measurements of corresponding properties of the other photon, even if the two entangled photons are separated by a distance.
  • the quantum mechanical state of an entangled-photon pair cannot be factored into a product of two individual quantum states.
  • more than two photons may be entangled together. More than two photons entangled together are referred to as "multiply-entangled” photons. Measuring properties of one or more photons in a set of multiply-entangled photons restricts properties of the rest of the photons in the set. As understood by those of ordinary skill in the art and by way of non-limiting example, the quantum mechanical state of a set of ri>2 multiply-entangled photons cannot be factored into a product of n separate states.
  • the term "entangled photons” refers to both biphotons and multiply- entangled photons.
  • Photon properties that may be entangled include time, frequency, polarization, and angular momentum.
  • photons that are entangled in time are referred to as “temporally-entangled photons.” Such photons are generated nearly simultaneously. For given optical path lengths traveled by constituent photons in a temporally-entangled photon pair, detecting one of the photons places limits on the times at which the other photon may be detected.
  • One aspect of the present invention provides a distance-determining system and method based on entangled photons that is substantially immune to detection by others.
  • a system for and method of determining a distance to an object includes generating a first photon and a second photon, the first photon and the second photon being entangled.
  • the first photon is directed at an object.
  • the first photon is received after being reflected off of the object.
  • the second photon is caused to travel a known distance.
  • the first photon and the second photon are directed to an entangled photon sensitive material.
  • An entangled-photon absorption of the first photon and the second photon is detected by the entangled photon sensitive material.
  • a distance to the object is found based on at least the known distance and the detecting.
  • the second photon may be caused to travel a known distance by using a bank of delays.
  • the first photon and the second photon may be directed to an optical cavity.
  • the first photon and the second photon may be directed to a first cavity or a second cavity.
  • An adjustable delay may be used.
  • a system for and method of determining a distance to an object is disclosed.
  • the method includes generating a first photon and a second photon simultaneously.
  • the first photon is directed at an object.
  • the first photon is received after being reflected off of the object.
  • At least the second photon is caused to enter an optical cavity.
  • An arrival of the first photon and an arrival of the second photon are detected.
  • the detection is used to determine a distance to the object.
  • the detection may include detecting using electronic photon detectors.
  • the detection may include detecting using an entangled photon sensitive material.
  • a system for and method of finding a distance to an object includes generating a plurality of first photons and a plurality of second photons, each of the plurality of first photons being associated with one of the plurality of second photons. At least a first portion of the first photons is directed to the object. A reflected portion of the first photons is received after being reflected off the object. At least a second portion of the second photons is directed to a cavity. A correlation between at least some photons in the reflected portion and at least some photons in the second portion is detected. The correlation is used to determine the distance to the object.
  • the detecting may include detecting using a coincidence counter.
  • the coincidence counter may detect a temporal correlation between arrival times, at a first detector, of at least some photons in the reflected portion and arrival times, at a second detector, of at least some photons in the second portion.
  • the temporal correlation may include a temporal translation.
  • the detection may include detecting using a biphoton sensitive material.
  • the correlation may include spatial coincidence between the at least some photons in the reflected portion and the at least some photons in the second portion. The distance to the object may be found as a remainder of the distance to the object upon being divided by a length of the cavity.
  • At least a third portion of the second photons may be directed to a second cavity.
  • a second correlation between at least some photons in the reflected portion and at least some photons in the third portion may be detected.
  • the correlation and the second correlation may be used to determine the distance to the object.
  • At least a third portion of the photons in the second portion may be delayed.
  • the method may include spectral filtering.
  • a binary coil bank may be used.
  • the first photon is received after being reflected off of the object.
  • the second photon is caused to travel a known distance. At least the second photon is caused to enter an optical cavity. An arrival of the first photon and an arrival of the second photon are detected.
  • a distance to the object modulo the cavity length parameter based on at least the known distance and the detection is found.
  • the distance to the object modulo the cavity length parameter is used to determine the distance to the object.
  • the distance may be less than the cavity length parameter.
  • the cavity length parameter may be the optical length of an optical cavity.
  • the cavity length parameter may be a length associated with a plurality of optical cavities.
  • the length associated with a plurality of optical cavities may be an effective cavity length.
  • a system for and method of processing entangled photons includes selecting a wavelength.
  • a cavity is configured to have a cavity length.
  • the cavity has cavity mirror parameters.
  • the cavity length and the selected wavelength have a ratio, which is divisible by ⁇ after being adjusted for the cavity mirror parameters.
  • a plurality of photons are directed to the cavity.
  • An entangled photon pair is detected, the entangled photon pair including a first photon and a second photon, the first photon having a first frequency and the second photon having a second frequency.
  • the sum of the first frequency and the second frequency corresponds to the selected wavelength.
  • Fig. 1 is a schematic diagram depicting an entangled-photon range finder embodiment
  • Fig. 2 is a graph showing coincidence probability relative to distance from nominal range according to an embodiment of the present invention
  • Fig. 3 is a schematic diagram depicting range ambiguity for two different cavity lengths according to various embodiments of the present invention
  • Fig. 4 is a schematic diagram depicting an optical cavity according to an embodiment of the present invention
  • Fig. 5 is a schematic diagram depicting an entangled-photon range finder embodiment
  • Fig. 6 is a schematic diagram depicting a delay coil bank according to an embodiment of the present invention
  • Fig. 7 is a schematic diagram depicting an adjustable delay according to an embodiment of the present invention.
  • Fig. 8 is a schematic diagram depicting a two-cavity entangled-photon range finder embodiment
  • Fig. 9 is a graphical depiction of using two partial distance resolutions to achieve a complete distance resolution according to an embodiment of the present invention.
  • Fig. 10 is a schematic diagram depicting a two-cavity entangled-photon range finder embodiment
  • Fig. 11 is a schematic diagram depicting an electronic coincidence counter entangled-photon range finder embodiment
  • Fig. 12 is a schematic diagram depicting an optical cavity configuration for an entangled-photon range finder embodiment
  • Fig. 13 is a schematic diagram depicting a spectral filtering optical cavity configuration according to an embodiment of the present invention.
  • Fig. 14 is a graph depicting a signal-to-noise ratio as a function of mirror reflectance according to various embodiments of the present invention.
  • DETAILED DESCRIPTION [0036] The particulars shown herein are by way of example and for purposes of illustrative discussion of the exemplary embodiments of the present invention only and are presented in the cause of providing what is believed to be the most useful and readily understood description of the principles and conceptual aspects of the present invention. In this regard, the description taken with the drawings provides a fundamental understanding of the present invention, making apparent to those skilled in the art how the several forms of the present invention may be embodied in practice.
  • Figure 1 depicts an embodiment of an entangled-photon range finder 100.
  • Entangled-photon range finder 100 includes a coherent light source 120 (e.g., a laser), which provides pump beam 125.
  • Pump beam 125 is directed to nonlinear crystal 130 (e.g., beta barium borate), which type-II parametrically down converts the photons of pump beam 125 into entangled-photon pairs that are separated (e.g., using a polarizing beam splitter, not shown) into signal photons 140 and idler photons 145.
  • Signal photons 140 are directed to the object whose range is to be determined (the "target object") using optical techniques known to those of ordinary skill in the art. The target object reflects back a portion of signal photons 140 to entangled-photon range finder 100.
  • p s AI(4 ⁇ tz l )
  • Idler photons 145 are directed to coiled polarization-preserving fiber 150.
  • Fiber 150 sets the nominal range of the entangled-photon range finder embodiment. That is, fiber 150 delays idler photons 145 by an amount of time that corresponds to the estimated mean time it takes signal photons to arrive at, and return from, the target object.
  • the second photon of an entangled-photon pair to enter optical cavity 110 enters while the first photon of the pair to enter remains in optical cavity 110.
  • Fiber 150 serves to ensure that signal photons 140 and idler photons 145 enter optical cavity 110 at approximately the same time by delaying entry of the idler photon to correspond with the delay resulting from the signal photon traveling to, and returning from, the target object.
  • Optical cavity 110 is configured to temporarily trap entering signal photons 140 and idler photons 145 by continuously reflecting them back-and-forth inside the cavity.
  • Optical cavity 110 has high-quality mirrors 112, 114 (e.g., at least 99% reflectance).
  • mirrors 112, 114 are concave with foci set to ensure that photons remain inside optical cavity 110.
  • a photon's probability of remaining inside optical cavity 110 drops to about 1/e after it is reflected back and forth inside optical cavity 110 approximately 1/(7 ⁇ +2 ⁇ ) times, where T ⁇ , T 2 are the transmittance of mirrors 112, 114, respectively.
  • a photon's lifetime inside optical cavity 110 is approximately 2E c /c(T ⁇ +r 2 ), where L c is the length of optical cavity 110.
  • a typical photon' s lifetime in an optical cavity is, by way of non-limiting example, on the order of 10 "8 seconds for mirrors with a 1% transmittance.
  • Optical cavity 110 contains biphoton sensitive material (“BSM”) 115.
  • BSM 115 absorbs entangled-photon pairs with a high probability and allows single photons and random photon pairs to pass through with very low probability of being absorbed.
  • BSM 115 is therefore essentially transparent to all photons except biphotons.
  • both photons of an entangled-photon pair must be incident on the same atom or molecule of BSM 115 within the entanglement time in order to be absorbed.
  • an atom or molecule of BSM 115 ejects a fluorophoton, which maybe detected to indicate an entangled-photon pair absorption.
  • BSM 115 One or more suitable detectors in conjunction with BSM 115 thus detect a correlation between signal photons 140 and the idler photons 145 with which they are entangled.
  • a detailed description of BSM 115 is found in U.S. Utility Patent Application No. 10/850,394, to Kastellaet ⁇ /., filed on May21, 2004.
  • BSM 115 maybe, by way of non- limiting example, rubidium-87.
  • An individual detector 170 registering an entangled-photon absorption at its associated resolution cell indicates the location at which the signal photon has traveled essentially the same distance as the idler photon. Thus, registering an entangled-photon absorption provides an indication of distance to the target object.
  • Each detector is functionally connected to a computer, which processes detection information as described herein.
  • the distance to the target obj ect is resolved up to an integer number of cavity lengths L c (i.e., modulo the cavity length) according to the following.
  • / represents the detector region in which both signal and idler photons are first present together, where the detectors are enumerated such that the first detector is adjacent to aperture 180.
  • the symbol d 0 represents the distance to the target object.
  • the symbol d sys represents the idler photon optical path length prior to entering optical cavity 110, and includes, inter alia, the length of fiber 150.
  • the letter n represents the number of complete round trips made by the idler photon in optical cavity 110.
  • the symbol ⁇ represents the width of each resolution cell.
  • Equation (1) accordingly determines the distance d 0 of the target object except for an unknown number n of signal photon round-trips in the cavity.
  • the distance d 0 to the target object may be resolved modulo the cavity length to an accuracy of ⁇ by monitoring detectors 170 to determine j, plugging in known system parameters, and solving equation (1) for d 0 in terms of n.
  • This computation thus determines d mod L c , where the notation "a mod b" in general indicates the remainder left over after dividing a by b.
  • the ambiguity between which detector 170 detects the true first location/ at which the signal and corresponding idler photons are present together and which detector detects its conjugate/' may be resolved, by way of non-limiting example, as follows. Mechanically or electro-optically adjusting the path length d ⁇ will cause/ and / ' to change. Techniques for adjusting optical path length are discussed in detail below in reference to Fig. 5. If d ⁇ s is lengthened, / will increase and /' will decrease. Similarly, if d sys is shortened,/ will decrease and/ ' will increase. Thus, by perturbing the path length and monitoring detectors 170 for the positions of/ and/', the true resolution cell of first coincidence / will be identified.
  • Both photons of an entangled-photon pair preferably enter optical cavity 110 before the first photon of the pair to enter is either absorbed or exits optical cavity 110.
  • the depth of field i.e., the distance about the nominal range in which ranges may be determined
  • the photon lifetime inside of optical cavity 110 is one parameter that affects the ranges that may be measured by an entangled-photon range finder embodiment.
  • a target object that is within the depth of field of the nominal range will generally have its distance accurately determined.
  • the depth of field for the entangled-photon range finder embodiment centered about its nominal range (as determined in part by the length of fiber 150), may be approximated as, by way of non- limiting example: z --r (3)
  • Z Ph is the depth of field
  • L c is the length of optical cavity 110
  • R is the reflectance of mirrors 112, 114.
  • the biphoton coincidence amplitude decays to 1/e of its nominal value.
  • Depth of field may be used to avoid certain types of inaccurate range determinations.
  • near-field clutter may produce aberrant range determinations by reflecting signal photons before they reach the target obj ect. Such aberrations may be avoided by insuring that signal photons returning from such near-field objects do not survive in the cavity long enough to coincide with their idler photons.
  • a background to the target object such as clouds or the Earth's surface, mayreflect signal photons and produce aberrant range determinations. Such determination may be avoided by insuring that the idler photons do not last inside of the cavity long enough to coincide with signal photons returning from far beyond the target object. In both instances described in this paragraph, configuring the depth of field to insure that in some cases the signal and idler photons do not coincide avoids certain aberrant range determinations.
  • Fig. 2 is a graph depicting coincidence probability relative to target object distance from nominal range according to an embodiment of the present invention.
  • the nominal range is discussed above in reference to equation (3). If the target object is within the depth of field of the nominal range (within the nominal range ⁇ Z p ⁇ ,) then the probability of coincidence is at its highest. If the target object's distance from the nominal range is greater than the depth of field (outside of the nominal range ⁇ Z p ⁇ ,) then the probability of coincidence falls off dramatically. At twice the distance of the depth of field (more than ⁇ 2Z p/ i) from the nominal range, the probability of coincidence is statistically insignificant. [0050] Fig.
  • FIG. 3 depicts the effects on range finding of photon lifetime relative to differing cavity lengths 305 according to various embodiments of the present invention. If the depth of field is greater than the cavity length 305 as depicted at 320, the resulting significant range ambiguity will inhibit uniquely resolving the underlying range. This ambiguity results in an initial range determination that is plus or minus some integer multiple of the cavity length of the actual range. This is seen by noting that the curve 200 of Fig.2 (scaled downward in thej-axis direction) interposed at 300 as depicted at 320 covers multiple cavity lengths. Conversely, when the cavity length 305 is greater than the depth of field as depicted at 310, the range ambiguity becomes insignificant, allowing for the range to be fully and uniquely resolved.
  • the curve 200 of Fig 2 (scaled downward in the -axis direction and depicted 300 at 310) thus essentially fits within a single cavity length.
  • the use of larger cavity lengths can reduce the possibility of ambiguity and increase the likelihood of accurately measuring the range to target by increasing the effective cavity length to beyond the depth of field.
  • such an ambiguity may be accounted for and the actual range determined by any, or a combination of, modifying the nominal range, by computer processing (e.g. , looking for a sudden discontinuity in ranging that is some multiple of the cavity length), or by other methods.
  • optical cavity 410 is a schematic diagram of an optical cavity 410 according to an embodiment of the present invention.
  • the length of optical cavity 410 is selected to, ter alia, ensure a biphoton resonance condition.
  • the biphoton resonance condition maximizes the two-photon coincidence amplitude.
  • biphoton coincidence amplitude satisfies, by way of non-limiting example: ⁇ ⁇ ⁇ ⁇ ⁇ M ⁇ H ⁇ ⁇ t H4 2 )2 - ( )
  • T ⁇ is the time at which the signal photon is absorbed or detected
  • 7 ⁇ is the time at which the idler photon is absorbed or detected
  • s ⁇ is the total optical path length traveled by the signal photon
  • s 2 is the total optical path length traveled by the idler photon.
  • the symbol R c represents the average coincidence count rate
  • ) represents the biphoton wave function at the output surface of the crystal.
  • Equation (5) The parameters of equation (5) are the same as those of equation (4) with the following additions: ⁇ is a normalization constant, O p is the frequency of pump beam (e.g., 125 of Fig. 1), and ⁇ ⁇ ⁇ is the difference between signal photon and idler photon frequencies.
  • D is the difference in inverse group velocities of ordinary and extraordinary rays leaving a nonlinear crystal.
  • D is the difference in inverse group velocities of ordinary and extraordinary rays leaving a nonlinear crystal.
  • D is the difference in inverse group velocities of ordinary and extraordinary rays leaving a nonlinear crystal.
  • D ⁇ 0.2 psec/mm, where "psec" denotes picoseconds.
  • L is the length of the nonlinear crystal.
  • the product DL determines the entanglement time.
  • the incorporation of the rectangle function defined by equation (5) into equation (4) serves to indicate that if an idler photon is absorbed or detected at time r 2 , then, for equal optical path lengths the probability that the signal photon is detected at time T ⁇ is effectively zero for T ⁇ ⁇ r 2 or for Tj > T 2 + DL.
  • the probability amplitude also satisfies the following equation:
  • Equation (7) implies the following equation:
  • optical cavity 410 The biphoton probability amplitude inside of optical cavity 410 is calculated presently.
  • the signal and idler photons are assumed to enter the cavity from the same side with equal optical path lengths and with no attenuation.
  • Optical cavity 410 is characterized by the complex reflectance coefficients rj, r 2 and transmittance coefficients gi, g 2 of the two mirrors 412, 414, respectively.
  • the biphoton amplitude, A cav (t- ⁇ , t, x), is generally zero unless, by way of non-limiting example:
  • the biphoton amplitude becomes, by way of non-limiting example:
  • the wavelength of a biphoton may be characterized as the speed of light divided by the sum of the signal photon frequency and idler photon frequency.
  • the biphoton resonance condition obtains when the left-hand-side of equation (12), represented by radians, is divisible by ⁇ .
  • the left-hand-side of equation (12) represents the cavity length divided by the biphoton wavelength and adjusted for the phases of the complex reflection coefficients for the cavity mirrors. Note that the frequencies of the individual photons in an entangled photon pair do not affect the biphoton resonance condition.
  • the probability of biphoton coincidence may be described as, by way of non-limiting example:
  • the cavity or pump frequency should be adjusted to account for the change.
  • the biphoton resonance condition can then be used to filter for a particular Doppler frequency in systems where relative motion is great enough to affect results. Relative motion between the range finder and target object may be accounted for in other ways, such as by limiting the integration time, or by sweeping an adjustable delay or coincidence delay ⁇ w .
  • optical cavity 410 in an entangled photon range finder embodiment has several advantages.
  • both the signal photon and the idler photon should be present together at the same BSM molecule within the entanglement time. Without a cavity, this could be accomplished by delaying the idler photon (e.g., using fiber 150) to precisely match the time it takes its corresponding signal photon to propagate to and be reflected from the target object.
  • optical cavity 410 serves to fold the optical path that a photon takes back onto itself a large number of times, and the signal and idler photons have an opportunity to encounter each-other with each such fold.
  • Fig. 5 depicts an embodiment of an entangled-photon range finder 500 in which signal photons 540 and idler photons 545 propagate in the same direction in optical cavity 510 (i.e., the signal and idler photons enter from the same side).
  • Pump beam 525 is directed to nonlinear crystal 530, which causes pump beam photons 525 to split into entangled-photon pairs.
  • Fig.5 also depicts a dichroic beam splitter 535, which is placed so as to prevent any residual pump beam 525 leaving nonlinear crystal 530 from passing. Entangled-photon pairs are directed to polarizing beam splitter 565, which separates signal photons 540 from idler photons 545.
  • Signal photons 540 are directed to the target object and collected at aperture 580 upon being reflected.
  • Idler photons are directed to delay coil bank 590 and then to adjustable delay 595.
  • Idler photons 545 leaving adjustable delay 595 and signal photons 540 returning from the target object are passed into a combined beam 587 using polarizing beam splitter 585.
  • Combined beam 587 is directed to optical cavity 510.
  • Optical cavity 510 containing BSM 515 is monitored by detector 570. Because signal photons 540 and idler photons 545 propagate in the same direction, their absorption by BSM 515 may be detected throughout optical cavity 510 by detector 570.
  • Detector 570 may include, by way of non-limiting example, an avalanche photodiode or a photo multiplier tube.
  • Binary coil bank 590 is used to set the idler photon optical path to about the same length as twice the estimated distance to the target object. Binary coil bank 590 thus sets the nominal range of the entangled-photon range detector. In particular, each signal photon (e.g., 140) and the idler photon (e.g., 145) with which it is entangled preferably enters optical cavity 510 within the optical cavity lifetime of the first to enter. Further detail of binary coil bank 590 are presented below in reference to Fig. 6.
  • Adjustable delay 595 is set to produce maximal biphoton absorptions within the time interval from zero to 2E c /c. Maximal biphoton absorption coincides with each signal photon 540 entering optical cavity 510 or being reflected off mirror 517 within the entanglement time interval of the idler photon 545 with which it is entangled entering optical cavity 510 or being reflected off mirror 517. Maximal biphoton absorption also indicates that the total optical path length traveled by idler photons 545 equals the total optical path length traveled by signal photons 540.
  • the time adjustment, ⁇ , from adjustable delay 595 can be resolved to within a fraction of the entanglement time.
  • the entanglement length (the entanglement time multiplied by the speed of light) is analogous to resolution cell width ⁇ for this arrangement. If the length L c of optical cavity 510 is chosen to be a multiple M of the entanglement length, then maximal biphoton absorption will occur when lies in the y ' -th temporal interval of width ⁇ /c, where, by way of non-limiting example:
  • the partial range resolution can be on the order of 60 ⁇ m, resulting in a large number of effective resolution cells for a relatively short cavity length.
  • a photon accrues an additional 2E C path length. Therefore, maximal biphoton absorptions maybe achieved by selecting ⁇ from between zero and 2E c /c. That is, to determine a setting of adjustable delay 595 that maximizes biphoton absorption, it suffices to test values of ⁇ in the closed interval [0, 2E c /c].
  • Use of optical cavity 510 thus provides a concise search domain within which delay times may be selected to correlate the signal and idler photons.
  • Optical cavity 510 effectively limits the delay values that need to be tested to achieve maximal biphoton absorption. Further details of adjustable delay 595 are disclosed below in reference to Fig. 7. [0065] The distance to the target object resolved up to an unknown multiple of L c once biphoton absorptions are maximized as follows. The distance d sys traveled by idler photons 545 is known. Because d S y S +2nL c is within the entanglement distance (the distance that light can travel during the entanglement time) of o, the distance d to the target object may be determined modulo the cavity length by monitoring system parameters and computing, by way of non-limiting example: d sy J2 mod L c .
  • the quantity L c is the length of cavity 510
  • d sys is the system path length traveled by idler photons 545, including the delays introduced by binary coil bank 590 and adjustable delay 595 but not including the unknown number n of round trips in optical cavity 510.
  • the resulting number d sys l2 mod L c is within the entanglement length of do mod L c once internal system path lengths are accounted for. Because entanglement times on the order of picoseconds are possible, margins of error of less than one millimeter are contemplated.
  • the signal-to-noise ratio for the embodiment of Fig.5 is estimated presently.
  • the rate at which photons are detected has two contributions, one from the biphotons and one from random two-photon absorption.
  • the contribution from the biphotons may be represented as, by way of non-limiting example:
  • ⁇ & is the flux of biphotons and Lj is the length of the interaction region within the cavity.
  • the symbol p ee is the density matrix element for a BSM atom absorbing a photon pair, and the 'dot' represents a derivative with respect to time.
  • the symbol R represents the reflectivity of the cavity mirrors, which are assumed to be lossless for purposes of exposition.
  • the symbol c p represents the pump beam frequency.
  • CE ⁇ represents the electric field per photon of frequency O p .
  • the symbol A e represents the entanglement area and T e represents the entanglement time.
  • the symbol ⁇ represents the probability that a molecule excited via two-photon absorption emits a fluorophoton that is detected by the photo-detecting elements (i.e., the quantum efficiency).
  • the random two-photon absorption contribution to the detection rate may be represented as, by way of non-limiting example:
  • Equation (18) has the same meaning as those of equation (17), except w represents the radius for the signal photon and idler photon beams, ⁇ s represents the signal photon flux, and ⁇ , represents the idler photon flux.
  • w represents the radius for the signal photon and idler photon beams
  • ⁇ s represents the signal photon flux
  • ⁇ represents the idler photon flux.
  • Equation (19) has the same meaning as those of equation (18), except ⁇ represents the bandwidth of the signal photon and idler photon beams, and ⁇ represents the line width of the excited atomic state, that is, the width of the transition.
  • the signal-to-noise ratio for the embodiment of Fig. 5 may accordingly be approximated as, by way of non-limiting example:
  • Equation (20) The symbols of equation (20) are the same as those of equation (19), except that B represents the electronics bandwidth.
  • the electronics bandwidth B is the reciprocal of the integration time, where the "integration time” is the amount of time spent testing each particular adjustable delay setting.
  • the biphoton flux is equal to the signal flux, which differs from the idler flux yp s , the probability that a signal photon returns from the target object. Background-limited signal-to-noise is achieved when, by way of non-limiting example:
  • equation (21) The symbols of equation (21) are the same as those of equation (20).
  • the background-limited signal-to-noise ratio may be represented as, by way of non-limiting example:
  • ⁇ is the single photon absorption cross-section and ris the lifetime of the virtual state.
  • the other symbols of equation (22) are the same as those of equation (20).
  • a filter may be interposed before the optical cavity in order to prevent photons that are not of the appropriate frequencies from entering.
  • Fig. 6 depicts a delay coil bank 600 according to an embodiment of the present invention.
  • Delay coil bank 600 is used to set the nominal range (or center of the depth of view) of an entangled-photon range finder.
  • Each coil 610, 615, 620 is preferably polarization-preserving and may be independently switched into or out of the photon path. Switching may be performed, by way of non-limiting example, by electro- optical elements 630, which act as half- wave plates when activated, and pairs of polarizing beam splitters 640. When electro-optical elements 630 are not activated, photons travel through polarizing beam splitters 640.
  • each coil length is a power-of-two multiple of some length increment, which is preferably no greater than the depth of field (equation (3)).
  • Fig. 7 depicts an adjustable delay 700 according to an embodiment of the present invention.
  • Adjustable delay 700 includes a first mirror set 710 and a second mirror set 720.
  • Second mirror set 720 is translatable with respect to first mirror set 710.
  • the photon path of travel may be shortened or lengthened accordingly.
  • a photon beam entering adjustable delay 700 encounters first mirror set 710 and is diverted to second mirror set 720.
  • Second mirror set 720 reflects back photons to first mirror set 710, which returns the photons to the beam.
  • the increased distance provided by adjustable delay may be monitored using, by way of non-limiting example, interferometetry.
  • the particular arrangement for delaying photons disclosed by Fig.7 is not meant to be limiting; other apparatuses for delaying photons are also contemplated.
  • Fig. 8 depicts an entangled-photon range finder embodiment in which two relatively short cavities are used to synthesize a much longer effective cavity length.
  • a pump beam 820 is directed to a nonlinear crystal 825, which provides entangled photons that are separated into signal photon beam 840 and idler photon beam 845.
  • signal photons 840 are directed to the target object and their reflection is collected at aperture 880, and idler photons 845 are directed to polarization-preserving optical fiber 850, which delays idler photons 845 by an amount of time estimated to be about equal to the travel time of signal photon 840.
  • idler beam 845 is separated using a half-silvered mirror 852 into two paths, each of which is directed through adjustable delays 860, 861 to independent optical cavities 810, 820, respectively.
  • Optical cavities 810, 820 are constructed according to the following. Each optical cavity 810, 820 is filled with BSM 811 , 821 , respectively. Optical cavity 810 of length L c ⁇ is partitioned into M ⁇ resolution cells of width ⁇ . Preferably, the resolution cell width ⁇ is chosen as an integer number of photon wavelengths of pump beam 820. Each resolution cell is monitored for entangled-photon absorption by an associated detector 830.
  • optical cavity 820 of lengthJ c2 is partitioned into 2 resolution cells also of width ⁇ , each resolution cell being monitored for entangled-photon absorption by an associated detector 831.
  • the numbers of resolution cells in the respective optical cavities 810, 820 are preferably relatively prime O ' .e., the greatest common divisor and 2 is one). Both optical cavities satisfy the biphoton resonance condition stated according to equation (12) and the surrounding description.
  • Each optical cavity 810, 820 may be used to independently resolve the distance to the target object up to an integer number of respective cavity lengths (t.e., modulo Jci or J c2 , respectively).
  • adjustable delays 860, 861 maybe used to determine which resolution cell in each optical cavity corresponds to the resolution cell where signal photons and corresponding idler photons are first present together.
  • the resolution cells / ls / 2 where signal photons and corresponding idler photons are first present together in optical cavities 810, 820 may be determined.
  • equation (1) may be used to calculate do mod L c ⁇ and do mod L c .
  • the Chinese Remainder Theorem may be used to solve such systems of modular equations. Another technique for solving this system of modular equations is discussed below in reference to Fig. 9. [0078] For embodiments such as the embodiment of Fig. 8 with two cavities, a general formula governing preferable conditions emerges.
  • Fig. 9 graphically depicts how j ⁇ and / may be used to determine / e according to an embodiment of the present invention.
  • j ⁇ and/ 2 uniquely locate the position where signal photons and idler photons would first be present together in an effective optical cavity of length L ef - M 1 M 2 A.
  • two (or more) small optical cavities maybe used to simulate a larger effective optical cavity for range-finding purposes.
  • the larger effective cavity 930 and / ⁇ 940 may be represented graphically by laying 2 copies of first cavity 910 end-to-end next to Mi copies of second cavity 920.
  • the position of/i 915 is marked on each copy of first cavity 910, and the position of/ 2 925 is marked on each copy of second cavity 920.
  • the position/ ⁇ 940 in effective cavity 930 is where/i 915 and/ 2 925 align.
  • the distance to the target object may be computed as follows. For two cavities with Mi ⁇ 2 , and by way of non-limiting example, the following algorithm may be used to determine quantities q and q 2 , which are used to compute j e . r ⁇ - mod( 2 ,M j ) n +- M 1 -l while M ⁇ p ⁇ (nr + 1) M xP - ⁇ n ⁇ — int (27)
  • the distance d to the target object may then be determined (modulo L eJj ) by substituting the value of j eJ ⁇ determined using equation (28) and algorithm (27) into equation (25).
  • Resolution cell numbers Mi, M j are preferably relatively prime (t.e., the greatest common divisor ofM t and M j is one whenever i ⁇ j).
  • the Chinese Remainder Theorem maybe used to solve systems of modular equations toward determining the distance to the target object.
  • Fig. 10 depicts a two-cavity entangled-photon range finder embodiment. In the embodiment of Fig. 10, incoming signal photons pass through filter 1015 before entering cavity 1010. The embodiment of Fig. 10 is similar to that of Fig.
  • the signal photons and idler photons are synchronized. More particularly, the idler photons are delayed using adjustable delays 1060, 1061 by amounts of time sufficient to ensure that each idler photon is reflected off its respective mirror 1012, 1013 within the entanglement time interval of the signal photon with which it is entangled entering optical cavity 1010, 1020 or being reflected off mirrors 1012, 1013, respectively.
  • the signal photons propagate together with the idler photons with which they are entangled.
  • the two-cavity range finder embodiment of Fig. 10 may be used to resolve great distances using relatively short optical cavities.
  • the embodiment of Fig. 10 accomplishes this by simulating a relatively long effective cavity with two relatively short cavities.
  • the entanglement length is the effective resolution cell width ⁇ for this embodiment.
  • a device measuring less than one-quarter meter long may resolve distances of up to slightly more than a kilometer relative to the nominal range.
  • Fig. 11 depicts an electronic coincidence counter entangled-photon range finder embodiment 1100. Details of entangled range finder 1100 are similar to those of the embodiment of Fig. 5, except that an electronic coincidence counter 1150 is used to detect correlation between entangled signal and idler photons instead of a BSM. Similar to the embodiment of Fig. 5, idler photons 1145 leaving binary coil bank 1190 and signal photons 1140 returning from the target object are passed into a combined beam 1187 using polarizing beam splitter 1185. Combined beam 1187 is directed to optical cavity 1110. Photons leaving optical cavity 1110 through mirror 1127 are directed to polarizing beam splitter 1120.
  • Polarizing beam splitter 1120 separates signal photons 1140 from idler photons 1145.
  • Signal photons 1140 are directed to detector 1105, and idler photons are directed to detector 1115.
  • Detectors 1105, 1115 are electrically connected to electronic coincidence counter 1150.
  • Coincidence counter 1150 is configured to detect a correlation between signal photons 140 and the idler photons 145 with which they are entangled.
  • Coincidence counter 1150 may feed coincidence information to an internal computer or to an external computer.
  • Detection events at idler photon detector 1115 act as a trigger for a coincidence window. To account for path length difference between signal photons and idler photons, a coincidence delay is set electronically between the trigger and the start of the coincidence window.
  • an adjustable delay may be used such as that depicted in Fig. 5.
  • the coincidence window begins.
  • Coincidence counter 1150 registers a coincidence count whenever a detection event occurs at signal photon detector 1105 within the coincidence window.
  • Optical cavity 1110 provides several advantages in the electronic coincidence counter embodiment of Fig. 11 in that fine tuning may be accomplished electronically instead of, e.g., with optical delay 700 of Fig. 7.
  • the total delay time produced by binary coil bank and other spatial or electronic delays need not exactly equal the delay caused by the signal photon traveling to and returning from the target object in order to gain distance information. Instead, the distance to the target object is computed modulo the cavity length and multiple cavities are used to resolve the ambiguity.
  • optical cavity 1110 provides a concise search domain for delay times that correlate the signal and idler photons.
  • Optical cavity 1110 effectively limits the delay values that need to be tested. Without an optical cavity, correlation might require testing all possible delay values that a single photon may produce in traveling to and returning from a target object. With optical cavity 1110, test values are limited to a manageable interval.
  • Coincidence counter 1150 will generally register a coincidence count for every biphoton whose component photons are both detected. However, detection is a function of at least the quantum efficiency of detectors 1105, 1115. Typically, the coincidence window is larger than the entanglement time due to the speed of electronics. It is however possible to achieve coincidence windows that are on the order of a few tens of picoseconds.
  • the range resolution for the embodiment of Fig. 11 is dependent on the coincidence window length.
  • ⁇ represents the ranging resolution or accuracy and T c is the coincidence window length.
  • a typical coincidence count rate is estimated presently.
  • the biphoton coincidence count rate is the rate at which idler photons 1145 are detected multiplied by the probability that the corresponding signal photon 1140 is detected within the coincidence window.
  • the biphoton coincidence rate may be represented as, by way of non-limiting example:
  • ⁇ s and ⁇ are the quantum efficiencies of detectors 1105, 1115, respectively.
  • the terms s a ⁇ pi are the probabilities that the signal photon returns from the target and reaches detector 1105 and that the idler photon makes it through delay 1190, respectively.
  • the symbol -t represents the electronically-implemented coincidence delay.
  • T c represents the length of the coincidence window.
  • the symbol ⁇ & - represents the rate of biphoton generation.
  • the background coincidence count may be represented as, by way of non-limiting example:
  • Equation (35) the symbol ⁇ c ⁇ v is given as, by way of non-limiting example:
  • ⁇ represents the bandwidth of the entangled photons, which would be centered at aj p /2 for the degenerate case.
  • the symbol ⁇ ( ⁇ ) represents the power spectrum of the entangled photons. If the bandwidth is much greater than the free spectral range of optical cavity 1110, then for identical lossless mirrors, background coincidence count may be represented as, by way of non-limiting example: (1 -R) 2 ⁇ cc b ⁇ Ps sP biTc (37) (l + R)
  • the total coincidence count rate is the sum of the biphoton coincidence count rate (equation (32)) and the accidental count rate (equation (37)) and maybe represented as, by way of non-limiting example:
  • a particular adjustable delay setting or coincidence delay is deemed to be correct when it yields a maximum in the observed count rate. Such judgment may be performed automatically by suitable computer hardware or software.
  • Finding a ⁇ that maximizes the observed count rate determines the distance to the target object modulo 2E C .
  • Typical signal to noise rates for the embodiment of Fig. 11 are estimated presently.
  • the associated root-mean-square Poisson noise is proportional to the square root of the total count rate multiplied by the electronics bandwidth.
  • the signal-to-noise ratio may be written as, by way of non-limiting example: (39)
  • a signal is only present when 0( ⁇ , ⁇ w ) is non-zero. If the length of the coincidence window is much greater than the entanglement time, • t can be adjusted such that 0( ⁇ , ⁇ w ) is one.
  • the signal-to- noise ratio maybe estimated as, by way of non-limiting example:
  • the accidental-coincidence-limited case O ' .e., T c ⁇ bi » 1) may yield a suitable signal-to- noise ratio.
  • coincidence counter 1150 typically cannot distinguish between multiple events that arrive within the coincidence window. Therefore, the system is preferably operated in a regime where the number of detection events (on either detector 1105, 1115) in a coincidence window length is, on average, much less than one. This situation may be represented as, by way of non-limiting example:
  • a typical signal-to-noise ratio may be calculated using the following illustrative and non-limiting parameters.
  • the term "integration time” refers to the amount of time spent testing each coincidence delay setting.
  • integration time refers to the amount of time spent collecting data to be used for a calculation.
  • a sophisticated coincidence counter could evaluate, in a single integration time interval, each coincidence delay the size of a coincidence window partitioning the interval [0, 2L C ].
  • Fig. 12 depicts an optical cavity configuration for an entangled-photon range finder embodiment.
  • Fig. 12 depicts an arrangement of cavities for use in entangled-photon range finder embodiments that use an electronic coincidence counter to correlate signal photons with idler photons.
  • Incoming signal photons and idler photons 1205 are directed to polarizing beam splitter 1230.
  • Polarizing beam splitter 1230 reflects signal photons (dashed line) to quarter- wave plate 1235.
  • each quarter- wave plate generally serves to convert entering photons of one linear polarization into photons of another linear polarization at 90° to the first polarization upon the photons passing through the quarter-wave plate in one direction, being reflected, and passing back through the quarter- wave plate in the opposite direction.
  • Signal photons reflected from polarizing beam splitter 1230 enter quarter- wave plate 1235, which converts linearly-polarized photons to circularly-polarized photons and vice versa.
  • a portion of the circularly-polarized photons enters optical cavity 1210 of length L ⁇ , and a portion is reflected back to quarter-wave plate 1235.
  • Quarter-wave plate converts reflected circularly-polarized photons to linearly-polarized photons having an orientation at 90° to that of the originally entering signal photons, which allows them to pass through polarizing beam splitter 1230.
  • Incoming idler photons included in beam 1205 pass through polarizing beam splitter 1230, quarter- wave plate 1245, and onto optical cavity 1215 of length J ! .
  • a portion of these idler photons enter optical cavity 1215, and a portion are reflected back to quarter-wave plate 1245.
  • Quarter- wave plate 1245 changes the polarization of these idler photons such that they are reflected by polarizing beam splitter 1230 into combined signal photon and idler photon beam 1262.
  • Combined signal photon and idler photon beam 1262 reaches polarizing beam splitter 1265, which reflects idler photons (dotted line) to quarter- wave plate 1275 and passes signal photons (dashed line) to quarter- wave plate 1285.
  • a portion of the signal photons that pass through quarter-wave plate 1285 enter optical cavity 1225 of length L 2 , and a portion are reflected back through quarter wave plate 1285.
  • These reflected signal photons are reflected by polarizing beam splitter 1265 into beam 1298.
  • a portion of the idler photons that pass through quarter- wave plate 1275 enter optical cavity 1220 of length E 2 , and a portion are reflected back through quarter wave plate 1275.
  • the reflected idler photons pass through polarizing beam splitter 1265 and join the signal photons in combined signal photon and idler photon beam 1298.
  • Combined signal photon and idler photon beam 1298 may be directed to one or more subsequent optical cavity configurations.
  • Coincidence counters 1260, 1290 detect coincidence from their associated pairs of cavities.
  • Coincidence counter 1260 receives input from detectors 1250, 1255.
  • Detector 1250 detects the signal photons that pass through optical cavity 1210, and detector 1255 detects idler photons that pass through optical cavity 1215.
  • coincidence counter 1290 receives input from detectors 1280, 1295.
  • Detector 1280 detects the signal photons that pass through optical cavity 1225, and detector 1295 detects idler photons that pass through optical cavity 1220.
  • Each coincidence counter 1260, 1290 thereby detects coincidence between signal photons and idler photons.
  • Coincidence detector 1260 detects such coincidence after the photons have passed through optical cavities 1210, 1215 of lengthJi
  • coincidence detector 1290 detects such coincidence after the photons have passed through optical cavities 1220, 1225 of length L 2 .
  • the optical cavity configuration depicted in Fig. 12 may be used in conjunction with a variety of entangled-photon range finder embodiments.
  • the optical cavity configuration of Fig. 12 maybe inserted in the range finder embodiment of Fig. 11. More particularly, the configuration depicted in Fig. 12 may be substituted for the optical cavity 1110 in Fig. 11 by using the combined signal photon and idler photon beam 1187 as the combined signal photon and idler photon beam 1205.
  • the portion depicted in Fig. 12 replaces optical cavity 1110, its mirrors, and its detector 1150.
  • a combination using pairs of optical cavities is able to resolve ranges to target objects up to a relatively long effective cavity length in the manner describe above in reference to Figs. 8-10.
  • the configuration of Fig. 12 correlates signal photons with idler photons in a pair of cavities of identical lengthE
  • the configuration also correlates signal photons and idler photons in a pair of cavities of identical length L 2 .
  • L 2 For purposes of correlation, it makes no difference if signal photons and idler photons are present together in the same cavity or in different cavities of equal length. Accordingly, by choosing appropriate lengths and Li and E 2 , an effective cavity of much greater length may be synthesized as described above in reference to Figs. 8-10.
  • the optical cavity configuration of Fig. 12 has several advantages.
  • the mirrors used in optical cavities 1210, 1215, 1220, 1225 are highly reflective. Thus, most of the photons directed to the first pair of optical cavities 1210 and 1215 will be reflected and subsequently directed to the second pair of optical cavities 1220 and 1225. Most of these photons will be reflected and pass to combined signal photon and idler photon beam 1298. More correlations (e.g., those arising from optical cavities of a different length) maybe gathered by cascading additional optical cavity configurations, such as an optical cavity configuration of Fig. 12, after beam 1298.
  • Fig. 12 also has the advantage of avoiding using half-silvered mirrors to provide multiple combined signal photon and idler photon beams for multiple cavities of different lengths. While this technique may be used, it results in lower signal-to-noise ratios than can be achieved using the configuration of Fig. 12.
  • the optical cavity configuration of Fig. 12 also has many of the advantages of optical cavity 1110.
  • the configuration of Fig. 12 allows for flexibility in interposing a delay in that the signal photon delay need not be exactly matched. It also effectively limits the delay values that need to be tested to achieve correlation to a manageable interval.
  • Fig. 13 depicts a spectral filtering optical cavity configuration according to an embodiment of the present invention.
  • a combined signal photon and idler photon beam 1310 is directed to polarizing beam splitter 1315, which allows signal photons (dashed line) to pass through while reflecting idler photons (dotted line).
  • the signal photons pass through quarter wave plate 1320 to optical cavity 1325 of length L ⁇ .
  • the quarter-wave plates 1320, 1330, 1345, 1355 ofFig. 13 generally serve the same function as those of Fig. 12, namely, to convert entering photons of one linear polarization into photons of another linear polarization at 90° to the first polarization upon the photons passing through the quarter-wave plate in one direction, being reflected, and passing back through the quarter-wave plate in the opposite direction.
  • the idler photons reflected off of polarizing beam splitter 1315 pass through quarter wave plate 1330 to optical cavity 1335 also of length L ⁇ . Both signal and idler photons that are reflected by their respective cavities 1325, 1335 return to polarizing beam splitter 1315, which directs them to polarizing beam splitter 1340. Signal photons reflected off of polarizing beam splitter 1315 are reflected off of polarizing beam splitter 1340, through quarter- wave plate 1345, and to optical cavity 1350 of lengthEi. Idler photons passing through polarizing beam splitter 1315 also pass thorough polarizing beam splitter 1340, quarter wave plate 1355, and reach optical cavity 1360 of length L ⁇ .
  • Signal photons that leave optical cavity 1350 and idler photons that leave optical cavity 1360 are directed by polarizing beam splitter 1340 to combined signal photon and idler photon beam 1365, which may be directed to additional optical cavity arrangements.
  • additional optical cavity arrangement may be a spectral filtering optical cavity configuration as depicted in Fig. 13 having cavities of length E 2 different from Ei so as to synthesize a long effective cavity.
  • Detectors 1370, 1375 are configured to detect photons and report the same to coincidence counter 1380.
  • the configuration of Fig. 13 is designed to improve the signal-to-noise ratio by filtering out individual signal and idler photons that are resonant with the optical cavities.
  • the signal photon and idler photon fluxes may be represented as, by way of non-limiting example:
  • R is the reflectance of the mirrors (assumed for purposes of exposition to be lossless) for the first pair of optical cavities 1325, 1335 and R 2 is the reflectance of the mirrors for the second pair of optical cavities 1350, 1360.
  • the signal-to-noise ratio for the configuration of Fig. 13 is estimated presently. If the bandwidth is much greater than the free spectral range, the signal photon and idler photon fluxes can be approximated as, by way of non-limiting example: Under these circumstances, the accidental coincidence count rate may be approximated as, byway of non-limiting example:
  • the biphoton coincidence rate is accordingly reduced to, by way of non-limiting example:
  • the signal-to-noise ratio for the configuration of Fig. 13 maybe approximated as, by way of non-limiting example:
  • the spectral filtering configuration of Fig. 13 has at least two effects.
  • the first is a reduction in signal due to the loss of biphotons, which is a function of R ⁇ as evidenced by its appearance in the term in brackets in front of the square root in equation (46) .
  • the second effect is a significant reduction in the accidental coincidence rate relative to the biphoton coincidence rate, which improves the accidental- coincidence-limited signal-to-noise ratio. This is evidenced by the term in front of T c in equation (44), which is a function of both Rj and R 2 .
  • the advantages of the second effect make up for the loss of biphotons as per the first effect. A relatively higher flux may be required to reach the accidental-coincidence-limited case.
  • the spectral filtering configuration of Fig. 13 may be used in any of the previous electronic coincidence counter embodiments. By way of non-limiting example, it may be substituted for the optical cavity 1110 in the embodiment of Fig. 11. Further, it maybe cascaded with an additional spectral filtering configuration having cavities of a different length, for example to synthesize a long effective cavity.
  • the spectral filtering configuration of Fig. 13 has advantages similar to those of the other optical cavities and their arrangements. Byway of non-limiting example, it allows for flexibility in estimating the signal photon delay, in that the imposed idler photon delay (whether electronic or otherwise) need not be matched exactly. Further, it narrows the range of delay values to be tested to a manageable interval.
  • the signal-to-noise ratio may be improved by using multiply-entangled photons (e.g., entangled triples or generally, entangled ⁇ -tuples for ⁇ 2 of photons).
  • multiply-entangled photons e.g., entangled triples or generally, entangled ⁇ -tuples for ⁇ 2 of photons.
  • multiply-entangled-photon beam that includes one signal photon beam and two idler photon beams, with each signal photon entangled with two idler photons.
  • the signal photon beam is sent to the target object and its reflection is collected.
  • Each of the idler photon beams pass through identical delay elements and cavities before being detected, each at their own detector.
  • N represents the total number of entangled photons per entangled- photon set.
  • the N-photon coincidence rate may be approximated as, by way of non-limiting example:
  • Each additional entangled photon thus improves the discrimination against accidental coincidences by a factor of ⁇ uT c , which could be several orders of magnitude.
  • An advantage of the techniques described herein is that distances may be determined in a manner that is undetectable by third parties.
  • signal photons are sent to be reflected off of the target object.
  • the signal photons as used herein are broadband and relatively low-flux.
  • the signal and corresponding idler photon frequencies sum to a constant (the pump beam frequency), the frequencies of the individual signal and idler photons are distributed.
  • entangled-photon range finding does not require the emission of easily-detectible coherent radiation.
  • the techniques disclosed herein may be used to measure distances with minimal threat of detection by other parties.
  • the nominal range is preferably set to be approximately equal to the range to the target object. This may be accomplished by guessing or by other methods.
  • the nominal range may be set by using prior and/or real-time information about any, or a combination of, the target object's location, its momentum, its velocity, its physical condition, and its physical properties. Conventional range-finding methods that give a gross approximation of the target object's range may be used to set the nominal range, and the techniques discussed herein may be used to more accurately find the range once the nominal range is set.
  • portions of one embodiment maybe substituted, replaced, or inserted into other embodiments. That is, the teachings disclosed herein should be viewed collectively, with each embodiment capable of employing technologies drawn from other embodiments.
  • the following embodiment portions or features may be used in embodiments other than those with respect to which they are explicitly discussed: optical coil bank, electronic coincidence counter, BSM, same-direction infra-cavity photon propagation, different-direction infra-cavity photon propagation, multiple cavities, and synchronized signal and idler photons.
  • either the signal photons or the idler photons may be sent to the target object. If the idler photons are sent to the target object, the signal photons will be retained at the range finder and delayed using any of the techniques discussed herein. More generally, the terms “signal” and “idler” may be used interchangeably.
  • the embodiments disclosed herein may use sequential measurements.
  • the optical lengths of the cavity may be changed between measurements.
  • various cavities of different lengths or a bank of cavities may be interchanged for different measurements. Interchanging cavities may be accomplished by way of electro-optical -wave plates.
  • an iterative process may be employed where the range finding apparatus uses several different cavity lengths to home in on an object's distance.
  • entanglement time is a quantity associated with the spread in phase differences between signal and associated idler photons. That is, entanglement time relates to the collection of differences in phase between signal and associated idler photons produced by an entangled-photon source (e.g. , a non-linear crystal). Entanglement time may be, by way of non-limiting example, considered as the average time difference between when ordinary and extraordinary rays leave a nonlinear crystal. Ordinary rays leaving a nonlinear crystal are typically associated with signal photons, and extraordinary rays leaving a nonlinear crystal are typically associated with idler photons.
  • entanglement times on the order of T e 5 10 "13 seconds are possible with a crystal length of 5 mm.
  • Entangled photons may be produced according to a variety of methods. Those of ordinary skill in the art are capable of producing entangled-photon pairs, triples, etc.
  • entangled photons may be produced according to types I or II parametric downconversion. That is, biphotons whose constituent signal and idler photons are orthogonally polarized may be used as well as biphotons whose constituent signal and idler photons are polarized in parallel.
  • signal photons maybe separated from idler photons (and recombined with idler photons) using dichroic glass.
  • signal photons and idler photos may be selected as they exit the biphoton source by providing apertures at the appropriate angles.
  • Any nonlinear crystal not limited to BBO, may be used.
  • Other ways to produce entangled photons include: excited gasses, materials without inversion symmetry, and generally any properly phase-matched medium. Entangled-photon production consistent with this disclosure is not limited to using BBO or any other particular non-linear crystal. Furthermore, the entangled photons are not limited to any particular wavelength or frequency.
  • various indicia of entangled-photon absorption by the BSM may be used to detect entangled photons.
  • entangled-photon absorption may result in fluorescence, phosphorescence, direct electron transfer, or ionization of the absorbing material. Detecting fluorescence, phosphorescence, direct electron transfer, or ionization may be used to detect entangled-photon absorption.
  • avalanche photodiodes, photo multiplier tubes, or other devices may be used to detect the fluorophotons, ionization, direct electron transfer, or other absorption indicia.
  • the BSM is not limited to rubidium-87.
  • any material with appropriately structured energy levels such as cesium-133 ( 133 Cs) or other alkalis may be used.
  • such materials are those with a very narrow multi-photon absorption linewidth. More preferably, such materials are those with a very narrow multi-photon transition to an excited state that decays through a path that includes a radiative transition.
  • embodiments of the invention are not limited to any particular entangled-two-photon absorption or random-two-photon absorption electron energy level transition. Pump, signal, and idler photon frequencies and wavelengths may vary from those disclosed herein.
  • equations contained in this disclosure are illustrative and representative and are not meant to be limiting. Alternate equations may be used to represent the same phenomena described by any given equation disclosed herein. Li particular, the equations disclosed herein maybe modified by adding error-correction terms, higher- order terms, or otherwise accounting for inaccuracies, using different names for constants or variables, or using different expressions. Other modifications, substitutions, replacements, or alterations of the equations may be performed. [0121] The particular optical manipulation devices depicted herein are illustrative and representative and are not meant to be limiting.
  • prisms, apertures, filters, optical fiber, lenses, and particular lasers disclosed herein may be replaced with devices known to those of ordinary skill in the art.
  • Alternate embodiments of the present invention may delay one photon in various ways.
  • a length of optical fiber may be inserted into the path of one or both photons.
  • sets of mirrors may be used to increase the path length of one or both photons.
  • electronic detection delays O ' .e., coincidence delays maybe used.
  • Other techniques for delaying one or more photons may also be used.
  • Planck's constant h and the speed of light c may both considered to be one (1) for the purpose of calculations.
  • This convention allows, inter alia, for common units for frequency and energy, as well as common units for time and distance (e.g., temporal delays maybe considered as spatial lengths and vice versa).
  • This notational convention is accounted for after calculations have been performed in order to deduce correct units for application purposes.
  • This disclosure also uses Dirac bracket notation (e.g. ,

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Abstract

L'invention concerne un procédé destiné à déterminer une distance jusqu'à un objet. Un premier photon et un second photon sont générés simultanément. Le premier photon est réfléchi en dehors d'un objet. Le second photon est dirigé vers une cavité optique. L'arrivée du premier photon est corrélée avec l'arrivée du second, et la distance jusqu'à l'objet est au moins partiellement déterminée au moyen de la corrélation.
PCT/US2005/009853 2004-03-24 2005-03-24 Procede et systeme de telemetrie de photons enchevetres WO2005092071A2 (fr)

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EP1750145A3 (fr) * 2005-08-04 2010-01-06 Lockheed Martin Corporation Systèmes de radar et procédés utilisant des particules quantiques enchevêtrées
WO2008142389A1 (fr) * 2007-05-17 2008-11-27 Kabushiki Kaisha Toshiba Système optique créant des interférences entre photons
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WO2018224468A1 (fr) * 2017-06-09 2018-12-13 Robert Bosch Gmbh Procédé de fourniture d'un signal de détection pour des objets à détecter
CN113048969A (zh) * 2021-01-08 2021-06-29 中国船舶重工集团公司第七0七研究所 光纤陀螺用偏振纠缠光子对输出的小型纠缠源及调节方法

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