CN105259726A - Device and method for generating multi-frequency-point two-component entangled light field through continuous wave laser - Google Patents

Abstract

The quantum entangled state light field is an important resource for quantum precision measurement and quantum information research, is widely used in many fields of quantum information, and is of important value in the aspects of quantum key distribution, quantum communication network, quantum cryptography communication, quantum teleportation, quantum computing and the like. Currently, experimental schemes for generating the entangled state light field are mostly at a single frequency, or are the study of multi-component multi-color entanglement, and relate to the multi-optical-frequency entangled light field. The invention provides a device and method for generating the multi-frequency-point two-component entangled light field through continuous wave laser. Apart from being capable of generating entanglement at a zero frequency, the two-component entanglement can also have many frequency points simultaneously for quantum entanglement properties at a high frequency, and in this way, the maximally entangled state can be obtained. The device and method for generating the multi-frequency-point two-component entangled light field through continuous wave laser have the advantages of unique quantum property multi-channel, high efficiency, high channel capacity and the like, and will be one of the most important 'resources' in the field of quantum information.

Description

The device and method that multi-frequency point two component tangles light field is produced with continuous wave laser

Technical field

The present invention relates to lightfield compression state and Entangled State field, be specially a kind of continuous wave laser and produce the device and method that multi-frequency point two component tangles light field.

Background technology

Quantum Entangled States light field is the valuable source carrying out quantum precision measurement and quantum information research, all be widely used in many quantum information fields, as quantum key distribution, the preparation of continuous variable many components entangled, quantum communication network, quantum cryptography communication, there is very important value the aspect such as quantum teleportation and quantum calculation.The experimental program of current generation entangled is mostly single frequency section place, namely just centered by optical frequency, tangling within the bandwidth of chamber, or research is tangling of many components polychrome, be a kind of many optical frequencies tangle light field, namely utilize beam splitter coupling, cascade process, series connection, the way of optics cavity in parallel is tangled by optical parameter process implementation three to eight component.Above-mentioned technology also has certain limitation in quantum information application.Constrain the practical application of this technology.The tangling of single frequency point can cause quantum communication and quantum information channel quantity few, channel capacity is little.The many components of polychrome tangle the restriction that can be subject to low damage optical fiber in the long range propagation of reality, and its quantity is difficult to produce practical quantum information network.

Summary of the invention

The present invention solves to produce at present compression and the experimental program that tangles is all single frequency, or research is tangling of many components, cause lightfield compression state and Entangled State to also have the technical matters of certain limitation in quantum information application, provide a kind of continuous wave laser generation multi-frequency point two component to tangle the device and method of light field.

The device that a kind of continuous wave laser generation multi-frequency point two component of the present invention tangles light field realizes by the following technical solutions: a kind of continuous wave laser produces the device that multi-frequency point two component tangles light field; Described multifrequency is tangled generator and is comprised input coupled lens, exports coupled lens, is located at input coupled lens and the second order nonlinear crystal exported between coupled lens and PBS prism, PBS prism be located at export coupled lens emitting light path on; Described second order nonlinear crystal and export the primary optical axis that coupled lens all can tangle generator along multifrequency and move.

The method that a kind of continuous wave laser generation multi-frequency point two component of the present invention tangles light field adopts following technical scheme to realize: a kind of continuous wave laser produces the method that multi-frequency point two component tangles light field, comprise the steps: that a branch of continuous wave laser is tangled generator by inputting coupled lens input multifrequency by (a), continuous wave laser is exported by output coupled lens in second order nonlinear crystal after two quasi-nonlinear optical parameter processes, obtains the light field of multiple Frequency point; B the light field of multiple frequencies of () outgoing, by PBS prism, obtains multi-frequency 2 components in the transmission end of PBS prism and reflection end and tangles light field.

A branch of continuous wave laser is inputted in the chamber mirror of input coupled lens of the present invention, second order nonlinear crystal and output coupled lens composition and two quasi-nonlinear optical parameter processes can occur.Be two quasi-nonlinear optical parameter process schematic as described in Figure 1, wherein a ₀, b ₁, b ₂input mould, a ₁, a ₂inner chamber mould, export coupled modes; In the mirror of chamber, interactional Hamiltonian is:

χ in formula ⁽²⁾for Non-linear coupling parameter (i.e. second order nonlinear coefficient), determined by character such as the material of second order nonlinear crystal and matching ways; be respectively creation operator and annihilations operator.

In the ideal case, namely perfectly phase matching and without off resonance time, according to the Heisenberg's equation in quantum mechanics the equation of motion that can obtain signal light field and idle light field is:

For ease of calculating, by second nonlinear constant χ ⁽²⁾with the orthogonal mode α of pump field ₀merge into χ, 1 and 2 difference representation signal light and idle light.Suppose that the rate of decay of this two light field is identical, i.e. k ₁=k ₂=k, can draw light field multifrequency tangle generator intracavity round trip once after equation:

τ be light field in the multifrequency device cavity circulation time of one week, field operator can be expressed as the form of mean value and quantum fluctuation sum under steady state conditions, a reactor, namely α _ifor mean value, substitute into equation (4), (5) can obtain operator rise and fall equation:

By equation (6), (7) are through Fourier transform form $\mathrm{\δ}\hat{a}(t+\mathrm{\τ})\→\mathrm{\δ}\hat{a}\left(\mathrm{\ω}\right)e^{i\mathrm{\ω}\mathrm{\τ}},\mathrm{\δ}\hat{a}\left(t\right)\→\mathrm{\δ}\hat{a}\left(\mathrm{\ω}\right),$ Can obtain afterwards:

By calculating (8) and (9) formula, can obtain the fluctuating that multifrequency tangles generator inner chamber field is:

Boundary condition according to quadrature component undulation in frequency domain: wherein k is total rate of decay, is to be caused by the loss of interior cavity loss and output coupling mirror.(10) and (11) formula is substituted into boundary condition, multifrequency can be obtained after calculating and tangle the signal light field and the orthogonal amplitude of idle light field and orthogonal position phase that generator exports:

The orthogonal amplitude of definition input and output light beam and the fluctuating of orthogonal position phase are:

Pass through formula $V_{1\left(2\right)}^{out\&PlusMinus;}\left(\mathrm{\&omega;}\right)=<{\left|\mathrm{\&delta;}{\hat{X}}_{1\left(2\right)}^{\&PlusMinus;}\right|}^2>,V_{1\left(2\right)}^{in\&PlusMinus;}\left(\mathrm{\&omega;}\right)=<{\left|\mathrm{\&delta;}{\hat{X}}_{1\left(2\right)}^{in\&PlusMinus;}\right|}^2>,$ The variance of output light field orthogonal amplitude and orthogonal position phase can be obtained:

$V_1^{out\&PlusMinus;}\left(\mathrm{\&omega;}\right)={\left|\frac{k^2+{\mathrm{\&chi;}}^2-{\left(\frac{1-e^{i\mathrm{\&omega;}\mathrm{\&tau;}}}{\mathrm{\&tau;}}\right)}^2}{{(k-\frac{1-e^{i\mathrm{\&omega;}\mathrm{\&tau;}}}{\mathrm{\&tau;}})}^2-{\mathrm{\&chi;}}^2}\right|}^2{V}_1^{in\&PlusMinus;}+{\left|\frac{2k\mathrm{\&chi;}}{{(k-\frac{1-e^{i\mathrm{\&omega;}\mathrm{\&tau;}}}{\mathrm{\&tau;}})}^2-{\mathrm{\&chi;}}^2}\right|}^2{V}_2^{in\&PlusMinus;}---\left(15\right)$

$V_2^{out\&PlusMinus;}\left(\mathrm{\&omega;}\right)={\left|\frac{k^2+{\mathrm{\&chi;}}^2-{\left(\frac{1-e^{i\mathrm{\&omega;}\mathrm{\&tau;}}}{\mathrm{\&tau;}}\right)}^2}{{(k-\frac{1-e^{i\mathrm{\&omega;}\mathrm{\&tau;}}}{\mathrm{\&tau;}})}^2-{\mathrm{\&chi;}}^2}\right|}^2{V}_2^{in\&PlusMinus;}+{\left|\frac{2k\mathrm{\&chi;}}{{(k-\frac{1-e^{i\mathrm{\&omega;}\mathrm{\&tau;}}}{\mathrm{\&tau;}})}^2-{\mathrm{\&chi;}}^2}\right|}^2{V}_1^{in\&PlusMinus;}---\left(16\right)$

Subscript " in " in formula and " " out " represent input light field and output light field respectively, "+" and "-" represents orthogonal amplitude and orthogonal position phase respectively, and representation signal light and idle light are distinguished in subscript " 1 " and " 2 ".The calculated results of (15) and (16) formula of utilization, can show in mathematica program that multifrequency tangles the signal light field and the orthogonal amplitude of idle light field and the noise spectrum of orthogonal position phase that generator produces, the i.e. single armed noise spectrum of signal light field or idle light field, the result of their gained is identical.As shown in Figure 2,3.In Fig. 2, horizontal ordinate " ω " representative produces the frequency of light field, ordinate " " the signal light field that exports of representative and the orthogonal amplitude of idle light field and orthogonal position phase, subscript "+,-" representing orthogonal amplitude and orthogonal position phase respectively, subscript " 1,2 " is representation signal light and idle light respectively.Fig. 2 is the multiple Frequency point (ω=ω of signal light field and idle light field ₀, ω ₀± FSR, ω ₀± 2FSR, ω ₀± 3FSR, ω ₀± 4FSR, ω ₀± 5FSR) noise spectrum, illustrate that the orthogonal amplitude of signal light field and orthogonal position phase, the idle orthogonal amplitude of light field and the noise spectrum result of orthogonal position phase are identical.Fig. 3 is frequency is ω ₀place noise spectrum figure amplification display, in fact in Fig. 2 arbitrary frequency point place noise spectrum enlarged drawing all with frequency at ω ₀the noise spectrum enlarged drawing that place amplifies comes to the same thing.

The mutual often pair of corresponding Frequency point of two bundle single armed light fields all has quantum entanglement characteristic.As shown in Figure 4, the orthogonal amplitude of signal light field and the orthogonal amplitude of idle light field interrelated, the orthogonal position phase of signal light field is mutually interrelated with the orthogonal position of idle light field, and namely often pair, two-beam field Frequency point tangles mutually, and the correlated noise of gained is lower than shot noise limit.As shown in Figure 3.

The single armed noise spectrum of the first half representation signal light field of Fig. 4, the single armed noise spectrum of the idle light field of the latter half representative, two-beam field represents mutual Quantum Correlation by the intermediate symbol (symbol of " 8 " is coupled by the two-beam after PBS prism) being similar to " 8 ", and two components that namely generation multi-frequency point tangles tangle light field.

Consider the orthogonal amplitude of two output light fields and the Quantum Correlation (i.e. the difference of orthogonal amplitude sum and orthogonal position phase) of orthogonal position phase variance, utilize equation (14) to draw:

$V_{1out+2out}^{+}\left(\mathrm{\&omega;}\right)={\left|\frac{(k-{\mathrm{\&chi;}}^2)-{\left(\frac{1-e^{i\mathrm{\&omega;}\mathrm{\&tau;}}}{\mathrm{\&tau;}}\right)}^2}{{(k-\frac{1-e^{i\mathrm{\&omega;}\mathrm{\&tau;}}}{\mathrm{\&tau;}})}^2-{\mathrm{\&chi;}}^2}\right|}^2{V}_1^{in+}+{\left|\frac{(k-{\mathrm{\&chi;}}^2)-{\left(\frac{1-e^{i\mathrm{\&omega;}\mathrm{\&tau;}}}{\mathrm{\&tau;}}\right)}^2}{{(k-\frac{1-e^{i\mathrm{\&omega;}\mathrm{\&tau;}}}{\mathrm{\&tau;}})}^2-{\mathrm{\&chi;}}^2}\right|}^{2}V---\left(17\right)$

$V_{1out-2out}^{-}\left(\mathrm{\&omega;}\right)={\left|\frac{(k-{\mathrm{\&chi;}}^2)-{\left(\frac{1-e^{i\mathrm{\&omega;}\mathrm{\&tau;}}}{\mathrm{\&tau;}}\right)}^2}{{(k-\frac{1-e^{i\mathrm{\&omega;}\mathrm{\&tau;}}}{\mathrm{\&tau;}})}^2-{\mathrm{\&chi;}}^2}\right|}^2{V}_1^{in-}+{\left|\frac{(k-{\mathrm{\&chi;}}^2)-{\left(\frac{1-e^{i\mathrm{\&omega;}\mathrm{\&tau;}}}{\mathrm{\&tau;}}\right)}^2}{{(k-\frac{1-e^{i\mathrm{\&omega;}\mathrm{\&tau;}}}{\mathrm{\&tau;}})}^2-{\mathrm{\&chi;}}^2}\right|}^2{V}_2^{in-}---\left(18\right)$

The equation left side " " subscript "+" represent orthogonal amplitude, the orthogonal amplitude sum of subscript " 1out+2out " representation signal light and idle light, " " subscript "-" represent orthogonal position phase; the difference of the orthogonal position phase of subscript " 1out-2out " representation signal light and idle light; the i.e. correlated noise spectrum at two component light field multi-frequency point places; utilize formula (17) and (18); matching in mathematica software; the correlated noise that can obtain the orthogonal amplitude of multiple Frequency point and orthogonal position phase variance is composed, and is ω as Fig. 5 ~ Fig. 8 respectively schemes shown two-beam field in frequency ₀, ω ₀± FSR, ω ₀± 2FSR, ω ₀± 3FSR, ω ₀± 4FSR, ω ₀there is Quantum Correlation in ± 5FSR place, the correlated noise of two quadrature components is all lower than shot noise limit.According to the inseparability criterion that vanLoock-Furusawa proposes, δ ²(X ₁+ X ₂) < SNL, δ ²(Y ₁+ Y ₂) < SNL, can illustrate really there is multi-frequency point quantum entanglement between two component light fields, SNL represents shot noise limit.

In Fig. 5, Fig. 7, ordinate is the correlated noise spectrum of signal light field and idle light field variance, in Fig. 5 the orthogonal amplitude sum of signal light field and idle light field, in Fig. 7 it is the difference of the orthogonal position phase of signal light field and idle light field; In Fig. 6, Fig. 8, ordinate is signal light field and idle light field variance is ω in frequency ₀the amplification details display of place's correlated noise, in Fig. 6 that signal light field and idle light field show, in Fig. 8 in the amplification details of the orthogonal amplitude sum noise at zero frequency place that signal light field and idle light field show in the amplification details of the difference noise of the orthogonal position phase at zero-frequency place.In fact be ω in frequency ₀± FSR, ω ₀± 2FSR, ω ₀± 3FSR, ω ₀± 4FSR, ω ₀± 5FSR place amplify correlated noise spectrum result all with frequency at ω ₀the correlated noise spectrum that place amplifies is identical.

Further, the ratio by regulating the coupling bandwidth of second order nonlinear crystal and multifrequency to tangle the free spectral range of generator can control the Frequency point number of output light field; The free spectral range that described multifrequency tangles generator is determined by following formula: c/2L _cavity, L _cavityalso namely input coupled lens for chamber mirror length and export the spacing of coupled lens; The coupling bandwidth of second order nonlinear crystal is determined by following formula: 10c/L _crystal, wherein L _crystalfor the length of second order nonlinear crystal; The ratio that coupling bandwidth and the multifrequency of described second order nonlinear crystal tangle the free spectral range of generator is e, then multifrequency is tangled generator and can be produced e+1 Frequency point.

The invention allows for a kind of method that can obtain the output light field Frequency point quantity determined, and give above-mentioned concrete implementation method, make the present invention more can be widely used in reality.

Beneficial effect of the present invention: tangling of existing single frequency is at analysis frequency ω ₀=0 place produces and tangles, and makes to tangle the tangling the impact that is easily subject to laser technology noise of zero-frequency place and weaken.And our multifrequency is tangled not only to produce at zero-frequency place and is tangled, and can at high frequency treatment, as FSR, 2FSR, 3FSR, 4FSR....... place produces many light fields of tangling simultaneously.

The light field that " multifrequency tangles generator " can utilize continuous wave laser to produce multiple Frequency point to tangle, this proposition utilizing continuous wave laser generation multi-frequency point two component to tangle light field method, for multichannel quantum key distribution, the quantum information process that multimode is parallel, in many ways optimum Quantum Cloning state and quantum field of storage etc., be all very valuable unique quantum information resource, contribute to promoting further developing of quantum message area.

Accompanying drawing explanation

Fig. 1 bis-quasi-nonlinear optical parameter process schematic.

Fig. 2 is the noise spectrum of signal light field and the multiple Frequency point of idle light field.

Fig. 3 is frequency is ω ₀the amplification display figure of place's noise spectrum figure.

The single armed noise spectrum of the signal light field that Fig. 4 device of the present invention produces and idle light field.

Fig. 5 is the orthogonal amplitude sum schematic diagram of signal light field under multiple Frequency point and idle light field.

Fig. 6 is signal light field and the idle light field amplification details display figure at the orthogonal amplitude sum noise at zero frequency place.

Fig. 7 is the differential intention of the orthogonal position phase of signal light field under multiple Frequency point and idle light field.

Fig. 8 is signal light field and the idle light field amplification details display figure at the difference noise of the orthogonal position phase at zero-frequency place.

The structural representation of Fig. 9 device of the present invention.

Figure 10 the method for the invention produces the schematic diagram of 61 Frequency points.

Figure 11 the method for the invention produces the schematic diagram of 31 Frequency points.

In figure, 1-inputs coupled lens, 2-second order nonlinear crystal, and 3-exports coupled lens, 4-PBS prism.

Embodiment

Described second order nonlinear crystal 2 and output coupled lens 3 are installed on precise controlling translation stage.Be convenient to the movement both regulating like this, to realize the output of multiple Frequency point light field.

Optical cavity length is 3cm-6cm, namely chamber length can move realization by automatically controlled output coupled lens 3, scope be 0-30mm, the second order nonlinear crystal length in chamber is 2 ± 0.2cm, crystal moves 1.5cm by electronic control translation stage, and its position will be mated with output coupled lens 3.

The Frequency point number of tangling that two components that continuous wave laser produces after " multifrequency tangles generator " tangle light field depends on that the phase matching bandwidth sum multifrequency of crystal tangles the free spectral range of generator, the effect that multifrequency tangles generator increases non-linear process, causes the spectral filtering of lower conversion two component output light field simultaneously.

Suppose that the II type-Ⅱphase matching bandwidth of crystal is 30-60 times of the free spectral range (FSR) in chamber, the transmissivity t=5% of output coupling mirror, when mobile output coupling mirror makes the long L in chamber _cavity=6cm, according to c/2L _cavitywhen can obtain free spectral range (FSR) for 2.5GHz, the long L of crystal _crystal=2cm, according to 10c/L _crystalthe phase matching bandwidth that can obtain crystal is 150GHz, and now the coupling bandwidth of crystal is 60 times of the FSR in chamber, and the number that can produce Frequency point is 61, is respectively ω ₀, ω ₀± FSR, ω ₀± 2FSR, ω ₀± 3FSR ... ω ₀± 30FSR, as shown in Figure 10.

Figure 10: horizontal ordinate represents frequency, is from left to right followed successively by ω ₀-30FSR, ω ₀-25FSR, ω ₀-20FSR, ω ₀-15FSR, ω ₀-10FSR, ω ₀-10FSR, ω ₀-5FSR, ω ₀, ω ₀+ 5FSR, ω ₀+ 10FSR, ω ₀+ 15FSR, ω ₀+ 20FSR, ω ₀+ 25FSR, ω ₀+ 30FSR is totally 61 Frequency points, and ordinate is orthogonal amplitude and the orthogonal position phase of flashlight or idle light.

When mobile output coupling mirror makes the long L in chamber _cavity=3cm, according to c/2L _cavitywhen can obtain free spectral range (FSR) for 5GHz, the long L of crystal _crystal=2cm, according to 10c/L _crystalthe phase matching bandwidth that can obtain crystal is 150GHz, and now the coupling bandwidth of crystal is 30 times of the FSR in chamber, and the number that can produce Frequency point is 31, is respectively ω ₀, ω ₀± FSR, ω ₀± 2FSR, ω ₀± 3FSR ... ω ₀± 15FSR, as shown in figure 11:

Figure 11: horizontal ordinate represents frequency, is from left to right followed successively by ω ₀-15FSR, ω ₀-10FSR, ω ₀-5FSR, ω ₀, ω ₀+ 5FSR, ω ₀+ 10FSR, ω ₀+ 15FSR, totally 31 Frequency points, ordinate is orthogonal amplitude and the orthogonal position phase of flashlight or idle light.

Claims (5)

1. produce with continuous wave laser the device that multi-frequency point two component tangles light field, it is characterized in that comprising multifrequency tangles generator; Described multifrequency is tangled generator and is comprised input coupled lens (1), exports coupled lens (3), is located at input coupled lens (1) and the second order nonlinear crystal (2) exported between coupled lens (3) and PBS prism (4), and described PBS prism (4) is located on the emitting light path of output coupled lens (3); Described second order nonlinear crystal (2) and export the primary optical axis that coupled lens (3) all can tangle generator along multifrequency and move.

2. produce with continuous wave laser the device that multi-frequency point two component tangles light field as claimed in claim 1, it is characterized in that, second order nonlinear crystal (2) and output coupled lens (3) are installed on precise electric control translation stage.

3. one kind produces with continuous wave laser the method that multi-frequency point two component tangles light field, adopt device as claimed in claim 1, it is characterized in that, comprise the steps: that a branch of continuous wave laser is tangled generator by inputting coupled lens (1) input multifrequency by (a), continuous wave laser is exported by output coupled lens (3) in second order nonlinear crystal (2) after two quasi-nonlinear optical parameter processes, obtains the light field of multiple Frequency point; B the light field of () multiple Frequency point, by PBS prism (4) coupling, obtains multi-frequency 2 components in the transmission end of PBS prism (4) and reflection end and tangles light field.

4. produce with continuous wave laser the method that multi-frequency point two component tangles light field as claimed in claim 3, it is characterized in that, the ratio tangling the free spectral range of generator by the coupling bandwidth and multifrequency regulating second order nonlinear crystal (2) can control the Frequency point number of output light field; The free spectral range that described multifrequency tangles generator is determined by following formula: c/2L _cavity, L _cavityalso namely input coupled lens (1) for chamber mirror length and export the spacing of coupled lens (3); The coupling bandwidth of second order nonlinear crystal (2) is determined by following formula: 10c/L _crystal, wherein L _crystalfor the length of second order nonlinear crystal (2); The ratio that coupling bandwidth and the multifrequency of described second order nonlinear crystal (2) tangle the free spectral range of generator is e, then multifrequency is tangled generator and can be produced e+1 Frequency point.

5. produce with continuous wave laser the method that multi-frequency point two component tangles light field as claimed in claim 4, it is characterized in that, chamber mirror length adjusting range is 3cm-6cm, namely mirror length in chamber can realize by automatically controlled output coupled lens (3) is mobile, the scope exporting coupled lens (3) movement is 0-30mm, second order nonlinear crystal (2) length in chamber is 2 ± 0.2cm, second order nonlinear crystal (2) removable 1.5cm, and its position will be mated with output coupled lens (3).