JP4090459B2 - Polarization entangled photon pair generator - Google Patents

Description

  The present invention relates to a polarization-entangled photon pair generation device, and more particularly to a polarization-entangled photon pair generation device that generates a photon pair having a quantum mechanical correlation with respect to polarization.

  In recent years, quantum information communication systems using quantum mechanics such as quantum cryptography and quantum teleportation have been proposed. Quantum cryptography is a cryptographic scheme that distributes keys in a common key cryptosystem using the fact that physical quantities cannot generally be observed without changing the quantum state. The security of cryptographic keys is based on the principle of quantum mechanics. It is an extremely secure cryptographic communication system guaranteed by. Quantum teleportation is a system for transferring a quantum state, and is used for extending a transmission distance in quantum cryptography and for signal transfer in a quantum information processing apparatus such as a quantum computer.

  A photon pair (quantum entangled photon pair) having a quantum mechanical correlation is an important element in the quantum information communication system as described above. In order to transfer the quantum state of a photon by quantum teleportation, it is necessary to share a entangled photon pair between the sender and the receiver. By using the entangled photon pair, a quantum cryptography system suitable for long-distance transmission can be realized.

  A entangled photon pair having a quantum mechanical correlation with respect to various physical quantities is conceivable. Here, a entangled photon pair (hereinafter referred to as a polarization entangled photon pair) for a polarization state is assumed. Let | H> be the state of a single photon having lateral polarization (H polarization), and | V> be the state of a single photon having vertical polarization (V polarization). One of the photon pairs in the polarization entangled state is called a signal photon, and the other is called an idler photon, which are represented by subscripts s and i, respectively. At this time, the state of the polarization entangled photon pair is expressed by the following equation, for example.

  It is assumed that the signal-idler photon pair is separated and sent to observers A and B separated from each other, and both perform polarization measurement on the respective photons. The meaning of equation (1) is that if the observer A observes the H polarized wave | H>, the observer B always observes | H> for the photons paired therewith. Similarly, if the observer A observes the polarization | V>, the observer B always observes | V> for the photon paired therewith. In addition, Equation (1) uses the basis of HV polarization, but this is a basis using another basis, for example, clockwise circular polarization | R> and counterclockwise circular polarization | L>. Even if rewritten, the correlation with respect to the polarization of two photons is maintained.

  Since the quantum entanglement state in which the phase difference between the two product states is zero or π, as in the equation (1), the quantum mechanical correlation described above can be observed most significantly, the “maximally entangled state” Called entangled state). By skillfully using the quantum mechanical polarization correlation between two photons described above, quantum cryptography and quantum teleportation can be realized.

As a means for generating the above-mentioned polarization entangled photon pair, there is a method using a nonlinear optical effect. The second-order nonlinear optical medium, the pump light of frequency f _p is input,
f _p = f _s + f _i (2)
A signal photon having a frequency f _s satisfying the above and an idler photon having a frequency f _i are simultaneously generated. This phenomenon is called PDC (parametric down conversion). At this time, the following relationships hold among the phases φ _p , φ _s , and φ _i of the pump photons, signal photons, and idler photons.
φ _p = φ _s + φ _i (3)

Further, the third-order nonlinear optical medium such as an optical fiber, by entering the pump light frequency f _p, spontaneous emission FWM pump light is degenerated: by (SFWM spontaneous four-wave mixing) ,
2f _p = f _s + f _i (4)
Simultaneously generates idler photons signal photon and the frequency f _i of the frequency f _s satisfying. The following relationship holds between the phases of the pump photon, signal photon, and idler photon.
2φ _p = φ _s + φ _i (5)
When a certain type of nonlinear medium is used, when linearly polarized pump light is input, a signal-idler photon pair having the same linear polarization as that of the pump light can be generated through a PDC or SFWM process. For example, when H-polarized pump light is input, photon pairs represented by | H> _s and | H> _i are generated.

  FIG. 1 shows the operation principle of a conventional polarization entangled photon pair generator. In order to obtain polarization entanglement using PDC, a signal-idler photon pair having the same polarization as the pump light is generated for a linearly polarized pump light input in a specific axial direction. Two nonlinear media that do not generate photon pairs are prepared for orthogonally polarized pump light inputs (see, for example, Non-Patent Document 1). This nonlinear medium is arranged in series with the crystal axes tilted by 90 °. The first nonlinear medium 11 generates a signal-idler photon pair for 0 ° linearly polarized light (H polarized light) pump light input, and for 90 ° linearly polarized light (V polarized light). It is arranged by adjusting the axial direction so that nothing happens. On the other hand, the second nonlinear medium 12 is arranged so as to generate a signal-idler photon pair for a 90 ° linearly polarized pump light input and to generate nothing for a 0 ° linearly polarized light. Has been.

45 ° linearly polarized pump light is input to this nonlinear medium. 45 ° linearly polarized light can be decomposed into two components: 0 ° linearly polarized light and 90 ° linearly polarized light. Of these two components, the 0 ° linearly polarized wave component generates an H polarized signal-idler photon pair represented by | H> _s | H> _i in the first nonlinear medium, and the 90 ° component. Generates a V-polarized signal-idler photon pair represented by | V> _s | V> _i .

Here, the intensity of the pump light is made sufficiently small so that the probability that the H-polarized photon pair and the V-polarized photon pair are generated simultaneously becomes sufficiently small. At this time, it is unknown until the measurement whether the photon pair obtained at the output is H-polarization or V-polarization. Therefore, the output state is a superposed state of | H> _s | H> _i and | V> _s | V> _i , that is, a polarization entangled state represented by the equation (1).

P.G.Kwiat, et, al., “Ultrabright source of polarization-entangled photons”, Physical Review A, Vol.60, No.2, pp.R773-R776, 1999

  In order to obtain a polarization entangled photon pair, a conventional polarization entangled photon pair generator needs to prepare two nonlinear media having the same characteristics. Further, there is a problem that it is difficult to generate a polarization entangled photon pair in a long wavelength band (1.3 μm band or 1.55 μm band) for the following reason.

  In order to generate photon pairs, it is necessary to match the phase velocities of pump light, signal photons, and idler photons in a nonlinear medium. Assuming that quantum information communication using such a polarization entangled photon pair is performed on an optical fiber network, it is desirable that the wavelength band of the photon pair is a long wavelength band, but in the conventional bulk type nonlinear medium, It is difficult to satisfy the phase matching condition in the long wavelength band.

  In order to solve this problem, a method of efficiently generating photon pairs by satisfying quasi-phase matching in a long wavelength band by using a waveguide nonlinear element having a periodically poled structure can be considered. If these waveguide nonlinear elements are arranged in series at an angle of 90 ° to each other, it is possible in principle to generate a polarization-entangled photon pair by the method described in FIG. At this time, it is necessary that the generation rates of the photon pairs in the first and second nonlinear media be equal.

  In order to make the generation rate of photon pairs equal, it is necessary to input the pump light equally to both waveguides as a fundamental waveguide mode. This condition is applied to two waveguides whose axial directions are orthogonal to each other. It is actually difficult to meet. Therefore, it is difficult to obtain a polarization-entangled photon pair in the long wavelength band by applying the waveguide type nonlinear element to the method shown in FIG.

  The present invention has been made in view of such problems, and an object of the present invention is to provide a polarization entangled photon pair generating device that generates a polarization entangled photon pair in a maximum entangled state by one nonlinear medium. There is to do.

In order to achieve such an object, the present invention provides a pump light source that outputs pump light, which is an optical pulse train, and the pump light that is correlated with the polarization of each other. A nonlinear medium that outputs a certain signal photon and idler photon, an optical branching unit that branches a photon pair output from the nonlinear medium into two paths, and a pair of photons branched into the two paths are combined into the same path. Output optical multiplexing means and one of the two paths between the optical branching means and the optical multiplexing means, and the polarization state of the input photon pair is orthogonal to the input state And a polarization rotation means for converting into a state and outputting the difference, wherein the difference in optical propagation time between the two paths is set equal to the time interval of the optical pulse train .

According to a second aspect of the invention, the polarization entangled photon pair generating device according to claim 1, wherein at least one of the two paths, characterized in that it comprises an optical phase adjusting means for adjusting the phase of the light.

The invention described in claim 3 is characterized in that the nonlinear medium described in claim 1 or 2 is a nonlinear waveguide made of a nonlinear optical crystal.

According to a fourth aspect of the present invention, the nonlinear medium according to the first , second, or third aspect is an optical fiber having a nonlinear optical effect.

  As described above, according to the present invention, a polarization entangled photon pair in the maximum entangled state is generated by a simple configuration of one nonlinear medium and polarization rotation means provided in a Mach-Zehnder interferometer or Michelson interferometer. It becomes possible to do.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

FIG. 2 shows a polarization entangled photon pair generating apparatus according to Embodiment 1 of the present invention. V-polarized pump light having a coherence time represented by τ _p is input to the nonlinear medium 101. As the nonlinear medium 101, a waveguide nonlinear element, an optical fiber, or the like can be used. From the nonlinear medium 101, photon pairs represented by | t, V> _s and | t, V> _i are output. However, in | t, X>, t represents the photon pair generation time, and X (= V, H) represents the polarization state.

The obtained photon pair is a Mach-Zehnder (MZ) interferometer composed of two beam splitters (BS) 102 and 104, two mirrors 105 and 106, and a half-wave plate (HWP) 103. Is input. There is a difference in τ between the optical propagation times of the optical paths of the BS 102, the mirrors 105 and 106, and the BS 104 and the optical paths of the BS 102, the HWP 103, and the BS 104. The propagation time difference τ is set to satisfy the following condition with respect to τ _p and the coherent time τ _c of the signal photons and idler photons.
τ _c <τ <τ _p (6)

In addition to the above conditions, the time resolution of the photon counter used for the measurement must be smaller than τ _c . In the nonlinear medium 101, it is assumed that the probability that two or more photon pairs are generated within the coherent time τ _c of the signal-idler photon is sufficiently small and can be ignored.

  A half-wave plate (HWP) 103 is inserted in one optical path of the MZ interferometer. In the HWP 103, the input V-polarized light is converted to H-polarized light and output. When a signal photon or idler photon represented by | t, V> is input to the MZ interferometer, the following superposition state is obtained at a certain time t ′ as an output.

However, δ _x = ω _x τ, and ω _x is the angular frequency of the photon represented by the signal photon x = s or the idler photon x = i. In addition, amplitude terms common to all terms are omitted for simplicity (the same applies hereinafter). The first term indicates the component output through the optical path including the HWP 103 of the MZ interferometer, and the second term indicates the component output through the optical path including the mirrors 105 and 106, respectively. At this time, the state of the photon pair output from the interferometer at time t ′ is expressed by the following equation.

  In quantum cryptography and quantum teleportation, a pair of polarization entangled photons is received by two observers separated from each other (simultaneous counting). Therefore, the third and fourth terms that do not contribute to the coincidence counting in Expression (8) can be ignored. Therefore, only the first term and the second term remain by the simultaneous counting at time t ′, and the following polarization entangled state | Ψ ′ (t ′)> is obtained.

Here, in order for the quantum mechanical polarization correlation to be observable, the fluctuation of the relative phase difference δ _s + δ _i between the two product states of Equation (9) must be small. For the following reasons, if the condition of Expression (6) is satisfied, the fluctuation of the relative phase difference is reduced, and a stable polarization entangled state can be obtained.

The relative phase difference δ _s + δ _i is rewritten as (ω _s + ω _i ) τ. Assuming that the angular frequency of the pump light is ω _p , when PDC is used as the nonlinear effect of signal-idler photon pair generation and when SFWM is used, the relative phase difference is expressed by the equations (2) and (3), respectively. It can be expressed as:
δ _s + δ _i = ω _p τ (PDC) (10)
= 2ω _p τ (SFWM) (11)
Under the condition of equation (6), the frequency fluctuation of the pump light can be considered to be sufficiently small within the coherent time τ, so the fluctuation of the relative phase difference δ _s + δ _i is small.

FIG. 3 shows a polarization entangled photon pair generating apparatus according to Embodiment 2 of the present invention. The configuration of the second embodiment is an MZ interferometer provided with the HWP 203 and has the same configuration as the first embodiment. As the pump light, a pulse train having a time interval τ equal to the propagation time difference between the two paths of the MZ interferometer is used. The relationship of equation (6) is established between the coherent time τ _p of the pump light and the coherent time τ _c of the signal photon or idler photon. Similarly to the case of the first embodiment, in the nonlinear medium 201, it is assumed that the probability that two or more photon pairs are generated within the coherent time τ _c of the signal-idler photon is sufficiently small and can be ignored.

  Let k be the number of the time slot of the signal-idler photon pair generated in a pulsed manner. At this time, the kth photon pair pulse passing through the optical path including the mirrors 205 and 206 of the MZ interferometer and the k−1th photon pair pulse passing through the optical path including the HWP 203 are output in the same time slot. Is output. Let the time slot number be m.

Let the photon pair of the kth time slot output from the nonlinear medium be | k, V> _s and | k, V> _i . Here, k in | k, X> (X = V, H) represents a time slot in which a photon pair is generated. With the MZ interferometer, | k, V> _x is

Is converted to However, x = s, i, and δ _x = ω _x τ. Using this, the output of the MZ interferometer in the mth slot is

It becomes. From the same argument as equation (9), the following polarization entangled state | Ψ ′ _m > is obtained by coincidence in the _mth slot of the output of the MZ interferometer.

  In the second embodiment, the use of continuous-pulse pump light is assumed. However, even if two continuous-pulse pump light is used, a polarization-entangled photon pair can be generated.

In equations (9) and (13), two product states (| t, H> _s | t, H> _i and | t−τ, V> _s | t−τ, V> _i in equation (9) are used. , There is a relative phase difference δ _s + δ _i between | k, H> _s | k, H> _i and | k−1, V> _s | k−1, V> _i ) in equation (13), In general, this is different from the ideal polarization entanglement state shown by the equation (1). In order to obtain an ideal polarization entanglement state, it is necessary to adjust the phase difference generated in the two optical paths of the MZ interferometer so that the relative phase difference becomes 0 or π.

  FIG. 4 shows a polarization entangled photon pair generating apparatus according to Embodiment 3 of the present invention. In the third embodiment, a phase shifter 307 that gives an adjustable phase shift Δθ to the optical path of the V polarization component is inserted into the MZ interferometer. In the third embodiment, the phase shifter 307 is added to the configuration of the first embodiment. However, the phase shifter 307 can be added to the second embodiment and the fourth embodiment described later.

The value of Δθ is adjusted by the phase shifter 307 so that δ _s + δ _i + Δθ = 0. Thereby, an ideal polarization entangled state as shown in the equation (1) can be obtained.

  FIG. 5 shows a polarization entangled photon pair generating apparatus according to Embodiment 4 of the present invention. The MZ interferometer of Example 1 shown in FIG. 2 is replaced with a Michelson interferometer. The Michelson interferometer includes a BS 402, mirrors 405 and 406, and a quarter wave plate (QWP) 407. The difference in light propagation time between the round-trip optical path including the mirror 405 and the round-trip optical path including the mirror 406 and the QWP 407 is set so as to satisfy τ in Expression (6).

  A quarter wave plate (QWP) 407 is inserted in one of the optical paths of the interferometer. The input V-polarized signal-idler photon pair reciprocates once in the optical path, passes through the QWP 407 twice, and returns to the BS 402 to be converted to H-polarized light. According to this configuration, as in the first embodiment, if the condition of Expression (6) is satisfied, the fluctuation of the relative phase difference is reduced, and a stable polarization entangled state can be obtained.

  Note that a Faraday rotation element that rotates the input polarization state by 45 degrees and outputs it can also be used as the polarization conversion means inserted into the interferometer. As in the second embodiment, a pulse train can be input as pump light.

It is a figure which shows the operation | movement principle of the conventional polarization entangled photon pair generator. It is a figure which shows the polarization entangled photon pair generator concerning Example 1 of this invention. It is a figure which shows the polarization entangled photon pair generator concerning Example 2 of this invention. It is a figure which shows the polarization entangled photon pair generator concerning Example 3 of this invention. It is a figure which shows the polarization entangled photon pair generator concerning Example 4 of this invention.

Explanation of symbols

101, 201, 301, 401 Nonlinear medium 102, 104, 202, 204, 302, 304, 402 Beam splitter (BS)
103, 203, 303 Half-wave plate (HWP)
105, 106, 205, 206, 305, 306, 405, 406 Mirror 307 Phase shifter 407 Quarter wave plate (QWP)

Claims (4)

A pump light source that outputs pump light that is an optical pulse train ;
A non-linear medium that inputs the pump light and outputs a signal photon and an idler photon that are correlated with each other's polarization;
Optical branching means for branching the photon pair output from the nonlinear medium into two paths;
Optical multiplexing means for multiplexing and outputting the photon pairs branched into the two paths to the same path;
A polarization that is inserted into one of the two paths between the optical branching means and the optical multiplexing means and that converts the polarization state of the input photon pair into a state orthogonal to the input state and outputs it. Wave rotation means ,
The polarization entangled photon pair generating apparatus characterized in that a difference in optical propagation time in the two paths is set equal to a time interval of the optical pulse train . The polarization entangled photon pair generating apparatus according to claim 1, further comprising an optical phase adjusting unit that adjusts a phase of light in at least one of the two paths. The polarization entangled photon pair generation device according to claim 1 or 2 , wherein the nonlinear medium is a nonlinear waveguide made of a nonlinear optical crystal. 4. The polarization entangled photon pair generating device according to claim 1 , wherein the nonlinear medium is an optical fiber having a nonlinear optical effect.

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