LU102075B1 - Temporal wheeler's delayed-choice demonstration apparatus and demonstration method - Google Patents
Temporal wheeler's delayed-choice demonstration apparatus and demonstration method Download PDFInfo
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Abstract
The present invention provides a temporal Wheeler's delayed-choice demonstration apparatus and demonstration method to demonstrate Wheeler's ideas in a hybrid system consisting of massive particles and massless photons. The cold atomic Raman quantum memory makes the heralded single-photon divided into a superposition of atomic collective excitation and leaked pulse, thus acting as a memory-based beam splitter. In addition, the adjustable proportion of the beam splitters can be realized by changing the relative proportion of the quantum random number generator, the storage efficiency of the second memory-based beam splitter, and the relative storage time of two memory-based beam splitters, so as to observe the wave-particle complementarity of light. Moreover, the temporal Mach-Zender interferometer enables two paths combined in a single-mode fiber, thus greatly simplifying the experimental configuration. Therefore, the present invention provides a temporal Wheeler's delayed-choice demonstration apparatus and demonstration method, which has a novel structure, is easy to construct and has strong anti-interference.
Description
APPARATUS AND DEMONSTRATION METHOD ; |
TECHNICAL FIELD The present invention relates to a temporal Wheeler's delayed-choice | demonstration apparatus and demonstration method based on cold atomic quantum memory, belonging to the field of optical information and quantum information technologies.
BACKGROUND Since the 17% century, there have been two contradictory theories in people's thinking about the nature of light, that is, the particle theory represented by Newton and the wave theory represented by Huygens. In the 1860s, Maxwell established the electromagnetic theory of light and proved that light is an electromagnetic wave. In 1905, Einstein developed the quantum theory of light and successfully explained the photoelectric effect, and thus the nature of light led to new thinking. Bohr proposed that wave-like behavior and particle-like behavior are complementary and the detection result determines whether the particle shows the wave-like behavior or the : particle-like behavior.
Nowadays the most intriguing features of wave-particle complementarity of light | are exemplified by the famous Wheeler’s delayed-choice experiment with linear optics, nuclear magnetic resonance, and integrated photonic device systems in the optical platform, in which the behavior of light determined by measurement choice is contrary to people's intuition. Until now, the delayed-choice experiments are demonstrated by either massless photons or massive particles such as atoms, however, there is no report demonstrating Wheeler’s ideas in a hybrid system which consists of photons and atoms simultaneously. Recently, studying wave-particle complementarity of massive particles, such as metastable hydrogen, spin interferometers with neutrons and atoms, has attracted many interests for a deep understanding of Bohr’s complementarity principle towards macroscopic systems, which also has a certain
2 / 25 LU102075 application prospect in the wave-particle superposition experiments with the spin excitation caused by different atoms.
SUMMARY An objective of the present invention is to provide a temporal Wheeler's delayed-choice demonstration apparatus and demonstration method, which has a novel structure, is easy to construct and has strong anti-interference, so as to demonstrate and verify the wave-particle complementarity of light. The present invention demonstrates Wheeler’s ideas in a hybrid system consisting of massive particles and massless photons, which has been not implemented in other experiments until now.
In order to achieve the above objective, the present invention adopts the following technical solution. | According to a first aspect of the present invention, a temporal Wheeler’s ; delayed-choice demonstration apparatus includes: a first two-dimensional magneto-optical trap la, wherein, the first two-dimensional magneto-optical trap la is configured to generate a Stokes photon and an anti-Stokes photon in a spontaneously four-wave mixing process; the Stokes photon is a first optical signal 2a, and the anti-Stokes photon is a second optical signal 2b; the first optical signal 2a and the second optical signal 2b are counter transmitted out of the first two-dimensional magneto-optical trap 1a; the second optical signal 2b is collected into a second single-photon counting module 4b to be detected through a first convex lens 3a; the first optical signal 2a is coupled into a first single-mode optical fiber 5a through a second convex lens 3b; a first pump light 6a and a second pump light 6b are orthogonal polarization, propagate counter collinearly, and are transmitted into the first two-dimensional magneto-optical trap la to generate the spontaneously four-wave mixing process; a small angle is formed between the first pump light 6a and the second optical signal 2b, and a small angle is formed between the second pump light 6b and the first optical signal 2a;
DE a second two-dimensional magneto-optical trap 1b, wherein, after being transmitted by the first single-mode optical fiber 5a, the first optical signal 2a passes through a third convex lens 3c, first enters the second two-dimensional magneto-optical trap 1b, is then transmitted out of the second two-dimensional magneto-optical trap 1b, and is coupled to a second single-mode optical fiber 5b through a fourth convex lens 3d; a first coupling light beam 7a is transmitted into the second two-dimensional magneto-optical trap 1b to adjust a storage time of the first optical signal 2a in the second two-dimensional magneto-optical trap 1b; a third two-dimensional magneto-optical trap le; wherein, after being transmitted by the second single-mode optical fiber 5b, the first optical signal 2a passes through a fifth convex lens 3e, first enters the third two-dimensional magneto-optical trap lc, is then transmitted out of the third two-dimensional magneto-optical trap 1c, and is collected into a first single-photon counting module 4a to be detected through a sixth convex lens 3f; a second coupling light beam 7b is transmitted into the third two-dimensional magneto-optical trap 1c to adjust a storage time of the first optical signal 2a in the third two-dimensional magneto-optical trap 1c; and an electro-optic modulator 8, wherein, the electro-optic modulator 8 is connected in the second single-mode optical fiber 5b; the electro-optic modulator 8 is configured to introduce a phase shift for the first optical signal 2a when the first optical signal 2a | is transmitted in the second single-mode optical fiber 5b.
Preferably, an alkali metal atomic ensemble is trapped in each of the first two-dimensional magneto-optical trap la, the second two-dimensional magneto-optical trap 1b and the third two-dimensional magneto-optical trap 1c. The alkali metal atomic ensemble in the first two-dimensional magneto-optical trap la is used to generate a heralded single photon. The alkali metal atomic ensemble in the second two-dimensional magneto-optical trap 1b and the alkali metal atomic ensemble in the third two-dimensional magneto-optical trap lc are used as memory-based beam splitters.
4 / 25 LU102075 Preferably, switching of the first pump light 6a and switching of the second pump light 6b are controlled by a first acousto-optic modulator 9a and a second acousto-optic modulator 9b, respectively. Switching of the first coupling light 7a and switching of the second coupling light 7b are controlled by a third acousto-optic modulator 9 and a fourth acousto-optic modulator 9d, respectively. All the acousto-optic modulators are modulated by an arbitrary function generator, respectively.
Preferably, an optical depth of the first two-dimensional magneto-optical trap 1a is 40, an optical depth of the second two-dimensional magneto-optical trap 1b is 35, and an optical depth of the third two-dimensional magneto-optical trap 1c is adjusted between 0 and 40. | Preferably, each of a length of the first single-mode optical fiber 5a and a length of the second single-mode optical fiber 5b is 200-250 meters.
Preferably, the alkali metal atomic ensemble is a rubidium atomic ensemble or a cesium atomic ensemble.
According to a second aspect of the present invention, a demonstration method for verifying a wave-particle complementarity of light using the aforementioned demonstration apparatus includes the following steps: step 1: controlling switching of a first pump light 6a and switching of a second pump light 6b by a first acousto-optic modulator 9a and a second acousto-optic | modulator 9b, respectively; wherein the first pump light 6a and the second pump light 6b of orthogonal polarization propagate counter collinearly into a first two-dimensional magneto-optical trap la to generate a spontaneously four-wave mixing process; generating a Stokes photon and an anti-Stokes photon by the first two-dimensional magneto-optical trap la in the spontaneously four-wave mixing process, wherein the Stokes photon is a first optical signal 2a, the anti-Stokes photon is a second optical signal 2b, and the first optical signal 2a and the second optical signal 2b are counter transmitted out of the first two-dimensional magneto-optical trap la; wherein a small angle is formed between the first pump light 6a and the second optical signal 2b, and a small angle is formed between the second pump light 6b and
SO the first optical signal 2a; collecting the second optical signal 2b into a second single-photon counting module 4b through a first convex lens 3a, and coupling the first optical signal 2a into a first single-mode optical fiber 5a through a second convex lens 3b; | step 2: making the first optical signal 2a from the first single-mode optical fiber Sa pass through a third convex lens 3c and then enter a second two-dimensional magneto-optical trap 1b, and adiabatically switching off a first coupling light beam 7a, wherein the first optical signal 2a is stored in the second two-dimensional magneto-optical trap 1b; after a programmable storage time, switching on the first coupling light beam 7a again, wherein the first optical signal 2a is released from the second two-dimensional magneto-optical trap 1b, and meanwhile, the first optical signal 2a is divided into a stored part and a leaked part in time domain, and the stored part and the leaked part constitute two arms of a temporal Mach-Zender interferometer, respectively;
step 3: making the first optical signal 2a from the second two-dimensional magneto-optical trap 1b coupled into a second single-mode optical fiber 5b through a fourth convex lens 3d to generate an optical delay; when the first optical signal 2a is transmitted in the second single-mode optical fiber 5b, generating a phase shift on the stored part by an electro-optic modulator 8;
step 4: making the first optical signal 2a transmitted from the second single-mode optical fiber 5b pass through a fifth convex lens 3e and then enter a third two-dimensional magneto-optical trap lc; controlling switching of the second coupling light beam 7b by a fourth acousto-optic modulator 9d to control insertion or
: removal of the third two-dimensional magneto-optical trap lc as a memory-based beam splitter in the experimental apparatus;
step 5: collecting the first optical signal 2a from the third two-dimensional magneto-optical trap 1c into a first single-photon counting module 4a through a sixth convex lens 3f; and step 6: sending an electrical signal from the second single-photon counting module 4b and an electrical signal from the first single-photon counting module 4a to a time-correlated single-photon counting system to measure a corresponding time-correlated function.
Preferably, in step 4, a relative proportion of a quantum random number generator can be varied to adjust a degree of the insertion of the third two-dimensional magneto-optical trap lc as the memory-based beam splitter in the experimental apparatus, so as to observe a change of a wave-particle behavior through a change of an interference intensity.
Preferably, in step 4, a Rabi frequency of the second coupling light beam 7b can be varied to adjust a storage efficiency of the third two-dimensional magneto-optical trap 1c, so as to observe a change of a wave-particle behavior through a change of an interference intensity.
Preferably, in step 4, a storage time of the third two-dimensional magneto-optical trap 1c can be varied, so as to observe a change of a wave-particle behavior through a change of an interference intensity.
The present invention has the following advantages.
The atomic quantum memory can coherently transfer a single photon to a quasiparticle consisting of a large number of ground-state atoms. Moreover, the quantum memory can also be exploited to construct a temporal beam splitter. Therefore, testing Wheeler’s ideals with the quantum memory enables us to extend the comprehension of complementarity associated with light and matter simultaneously. The present invention provides a new temporal Wheeler's delayed-choice demonstration apparatus and demonstration method. The cold atomic Raman quantum memory makes the heralded single-photon divided into a superposition of atomic collective excitation and leaked pulse, thus acting as a memory-based beam splitter. In addition, the adjustable proportion of the beam splitters can be realized by changing the relative proportion of the quantum random number generator, the storage efficiency of the second memory-based beam splitter, and the relative storage time of two memory-based beam splitters, so that intermediate states between the particle-like behavior and the-wave-like behavior are observed. Moreover, the temporal Mach-Zender interferometer enables two paths combined in a Ban single-mode fiber, thus greatly simplifying the experimental configuration. Therefore, the present invention provides a temporal Wheeler’s delayed-choice demonstration apparatus and demonstration method, which has a novel structure, is easy to construct and has strong anti-interference.
BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 shows a structural diagram of an experimental apparatus of the present invention.
Fig. 2 is a schematic diagram showing the observed wave-like behavior, particle-like behavior and intermediate states between them by adjusting the relative proportion of a memory-based beam splitter.
Fig. 3 is a schematic diagram showing the observed wave-like behavior, particle-like behavior and intermediate states between them by adjusting the storage efficiency of a memory-based beam splitter.
Fig. 4 is a schematic diagram showing the observed wave-like behavior, particle-like behavior and intermediate states between them by adjusting the storage time of a memory-based beam splitter.
In figures: 1a-first two-dimensional magneto-optical trap 1b-second two-dimensional magneto-optical trap 1c-third two-dimensional magneto-optical trap 2a-first optical signal 2b-second optical signal 3a-first convex lens 3b-second convex lens 3c-third convex lens 3d-fourth convex lens 3e-fifth convex lens 3f-sixth convex lens 4a-first single-photon counting module
4b-second single-photon counting module 5a-first single-mode optical fiber 5b-second single-mode optical fiber 6a-first pump light 6b-second pump light 7a-first coupling light beam 7b-second coupling light beam 8-electro-optic modulator 9a-first acousto-optic modulator 9b-second acousto-optic modulator 9c-third acousto-optic modulator 9d-fourth acousto-optic modulator
DETAILED DESCRIPTION OF THE EMBODIMENTS In order to clearly explain the technical solution of the present invention, the demonstration apparatus and the demonstration method of the present invention are described in detail with reference to specific embodiments in conjunction with the drawings. Embodiment 1 As shown in Fig. 1, a temporal Wheeler’s delayed-choice demonstration apparatus includes three two-dimensional (two-dimensional) magneto-optical traps 1a, 1b, lc. An alkali metal atomic ensemble is trapped in each two-dimensional magneto-optical trap, and the alkali metal atomic ensemble can be rubidium-85 : atomic ensemble or cesium atomic ensemble. Each two-dimensional magneto-optical trap is a Raman memory, wherein the atomic ensemble in the first two-dimensional magneto-optical trap 1a is used to generate a heralded single photon. The quantum memory served as a quantum device in the synchronization of quantum information can enable the photon pulse to separate in time domain, where the separated time interval and amplitude of photons can be arbitrarily configured. Therefore, the quantum memory can be considered as a dynamically configurable temporal beam —_— ee
: 9 / 25 LU102075 splitter. Herein, according to the present invention, two Raman memories (i.e, the second two-dimensional magneto-optical trap 1b and the third two-dimensional magneto-optical trap 1c) are used as two memory-based beam splitters (M-BS1 and M-BS2) to form a Mach-Zender interferometer in time domain. When the storage ‘ efficiency is less than 1, it divides the single-photon wave packet into an atomic part and a photon part.
Firstly, the first pump light 6a and the second pump light 6b are orthogonal polarization and are transmitted into the first two-dimensional magneto-optical trap la to generate a spontancously four-wave mixing (SFWM) process, and the first pump light 6a and the second pump light 6b propagate collinearly in the first two-dimensional magneto-optical trap 1a with an optical depth (OD) of 40. As shown in Fig. 1, the SFWM process in the first two-dimensional magneto-optical trap 1a produces Stokes and anti-Stokes photons, where the Stokes photon is the first optical signal 2a, and the anti-Stokes photon is the second optical signal 2b. Here, the first pump light 6a has a wavelength of 795 nm and a Rabi frequency of 2xx1.19 MHz, and the second pump light 6b has a wavelength of 780 nm and a Rabi frequency is 2nx14.79 MHz. The angle between the pump lights and the optical signals is preferably a small acute angle within 0-10°. Preferably, the angle between the pump lights and the optical signals is 2.8° to satisfy the double-photon phase matching condition to maximize the coincidence count. In addition, the wavelength of the first optical signal 2a, the wavelength of the second optical signal 2b, the wavelength of the first pump light 6a and the wavelength of the second pump light 6b satisfy the phase matching condition of the SFWM, therefore the wavelength of the first optical signal 2a is 795 nm, and the wavelength of the second optical signal 2b is 780 nm. The first pump light 6a and the second pump light 6b are controlled by the first acousto-optic modulator 9a and the second acousto-optic modulator 9b, respectively. The two pump lights are diffracted through the acousto-optic crystal of the acousto-optic modulators, so that the power, frequency and turn-off of the diffracted lights can be controlled. The input radio frequency signal can be generated by using arbitrary function generator (Tektronix,AFG3252), and the acousto-optic modulator ee
| 10 / 25 ‘ LU102075 can be modulated by adjusting the parameters of the input radio frequency signal.
According to the present invention, the first convex lens 3a with a focal length of 300 mm and the second convex lens 3b with a focal length of 300 mm are adopted to collect the second optical signal 2b and the first optical signal 2a, respectively. The second optical signal 2b is received by the second single-photon counting module 4b and its time-correlated function is measured. The second single-photon counting module 4b is the avalanche diode 2, i.e., PerkinElmer SPCM-AQR-15-FC, with a maximum dark count rate of 50/s. The first optical signal 2a of the heralded single photon is coupled into the first single-mode optical fiber 5a through the second convex lens 3b.
The first optical signal 2a is transmitted through the first single-mode optical fiber Sa, and is then collected through the third convex lens 3c with a focal length of 300mm and enters the second two-dimensional magneto-optical trap 1b. The atomic ensemble in the second two-dimensional magneto-optical trap 1b acts as a Raman memory. The specific storage process is as follows. The first optical signal 2a passes directly through the second two-dimensional magneto-optical trap 1b with an optical depth of 35, while the first coupling light beam 7a with a Rabi frequency of Q., =27x20.61 MHz and a beam waist of 2 mm is switched off adiabatically, and then a stored atomic collective excited state is obtained given by 1NmY em 1), +12), 11. also called as spin wave, where kg =k, —k,, is the , wave vector of atomic spin wave, À, is the vector of the first coupling light beam 7a, | and À, is the vector of the first optical signal 2a, 7 denotes the position of the in atom in the atomic ensemble in the second two-dimensional magneto-optical trap 1b. This state consists of a large amount of massive atoms, corresponding to the state of matter which is different from the state of single photon. After a programmable storage time, the spin wave is converted back into photonic excitation by switching on the first coupling light beam 7a again.
| The first optical signal 2a is divided into two parts by the memory-based beam I} À
11 / 25 LU102075 splitter M-BS1 (i.e. the second two-dimensional magneto-optical trap 1b), which has the following states: [WE Man | I) + Jn, | Ru) equation (1), where, 77, is the conversion efficiency of optical signal to spin-wave in the memory-based beam splitter M-BS1. The right two terms in equation (1) represent the split states corresponding to the leaked part |L) and stored part |R,) during the quantum storage process, respectively. The coefficients 1-77. and fn are the amplitude of these two parts, respectively. #l=w- Ar is the relative phase between the states | L) and |R,) with the storage time Ar. æ denotes the optical frequency of the stored part. The stored part |R,) corresponds to the atomic collective excited state, which is a state containing a large amount of massive atoms. The expression given by equation (1) corresponds to a superposition state of photon and atom, and thus it is not determined that whether the photon is transformed to the atomic state or leaked. | After the storage time of At=200 ns, the first coupling light beam 7a is switched on by controlling the third acousto-optic modulator 9c, and the spin wave in the second two-dimensional magneto-optical trap 1b is read out as |R).
The first optical signal 2a has a photon superposition state lw) 0 T= | LY + fie 4 | R), where, = Mu > Which is the total storage efficiency of the first optical signal 2a in the second two-dimensional magneto-optical trap 1b, including the efficiency 7, of the first optical signal 2a conversion to the spin wave and the efficiency 7,,,,., of the spin wave retrieval to the optical excitation. These two split photon wave packets separated in time domain are equivalent to the two arms of the interferometer.
Between the second two-dimensional magneto-optical trap 1b and the third two-dimensional magneto-optical trap 1c, the first optical signal 2a passes through the
12 / 25 LU102075 fourth convex lens 3d and is then coupled into the second single-mode optical fiber 5b, and an optical delay is about 1 ps, so as to increase the length of the interferometer. In order to make the photon meet the time delay requirements, the length of the single-mode optical fiber is not be less than 200 m, but since the excessive length of the optical fiber will lead to poor stability of the system, the length of the first single-mode optical fiber 5a and the second single-mode optical fiber 5b is preferably selected from the range of 200 m - 250 m. In this experiment, the length of the first single-mode optical fiber 5a and the second single-mode optical fiber 5b is 200 m. When transmitting in the second single-mode optical fiber 5b, the first optical signal 2a passes through the electro-optic modulator (EOM) 8. The electro-optic modulator 8 is configured to vary the relative phase between the two arms of the interferometer by modulating a phase shift on the stored part | R), so that the state becomes: lw) D flan | L) ++/me™ x | R) equation (2), where, @,oy is the added phase by the electro-optic modulator 8.
The first optical signal 2a transmitted from the second single-mode optical fiber 5b passes through the fifth convex lens 3e and then enters into the third | two-dimensional magneto-optical trap 1e. Once the leaked part arrives the third | two-dimensional magneto-optical trap lc, a random choice to insert or remove the 1 third two-dimensional magneto-optical trap 1c has been made to realize the Wheeler’s delayed-choice experiment, which is controlled by a quantum random number | generator (QRNG). The random number is generated by performing a logic gate ‘operation between an electrical signal obtained after detecting the Stokes photon and a 100 kHz transistor-transistor logic (TTL) signal generated by an arbitrary function generator. Intrinsically, the emission of a single photon is an SFWM process, thus the random number is generated in a quantum random process. The choice to insert or remove the memory-based beam splitter M-BS2 (i.e. the third two-dimensional magneto-optical trap 1¢) is controlled by the switching of the second coupling light beam 7b implemented by the fourth acousto-optic modulator 9d, which is randomly
13 / 25 LU102075 decided by the QRNG.
The first optical signal 2a from the third two-dimensional magneto-optical trap lc passes through the sixth convex lens 3f and is then received by the first single-photon counting module 4a, and its time-correlated function is measured. The measurement method of the time-correlated function is as follows: the first single-photon counting module 4a and the second single-photon counting module 4b are gated in the experimental window, and then the electrical signals from the first single-photon counting module 4a and the second single-photon counting module 4b are sent to a time-correlated single-photon counting system (TimeHarp 260) to measure their time-correlated function. The first single-photon counting module 4a is an avalanche diode with a maximum dark count rate of 25/s. All the six convex lenses used in the experiment of the present invention are configured to collect the light beam, enhance the interaction between the light and the atomic ensemble, and obtain a relatively high signal-to-noise ratio.
The whole system can be described by a density operator: Pp == wily, [+S 1y,Xw, | equation (3), where, |w,) and |,) are considered as a wave-like state and a particle-like state, respectively. The whole system is a classical mixture of the two states, that is, the first optical signal 2a has both a particle-like state and a wave-like state, which is also called wave-particle duality or wave-particle complementarity.
|w,) corresponds to the case that the memory-based beam splitter M-BS2 (i.e. the third two-dimensional magneto-optical trap 1c) is inserted, and thus the whole setup forms a closed Mach-Zender interferometer. After switching off the second coupling light beam 7b with a Rabi frequency of Q, = 2x x24.21, the leaked part is converted to the spin wave in the third two-dimensional magneto-optical trap 1c.
& represents the random probability of inserting the memory-based beam splitter M-BS2. |y,) can be denoted by: me
14 / 25 LU102075 92) D Man (V1 | L) +0 | R00) +, | R) equation (4), Then 18 the efficiency of the leaked part |L) in equation (2) conversion to the spin wave in the third two-dimensional magneto-optical trap lc.
After the same storage time of 200 ns (thus the relative phase 6, =8, =A@), the second coupling light beam 7b is switched on to retrieve the spin wave |R,) to the optical signal, and the photon’s behavior is checked by projecting the density matrix p to the | retrieval part | R) . Ultimately, the probability of photon has a function of: P(E, Poon) 0 & 11 Mon fi, + me +1=E)7, equation (5), in analogy to 7, 72*aconTostorea 3S the total storage efficiency of the optical signal in the third two-dimensional magneto-optical trap 1c, where 7... is the efficiency of the spin wave retrieval to the photonic excitation.
As shown in Fig. 2, the present invention illustrates the wave-particle complementarity corresponding to £ =001, respectively.
Fig. 2(a) corresponds to the case of the time-correlated function when & = 0%, Fig. 2(b) corresponds to the case of the time-correlated function when & =50%, and Fig. 2(c) corresponds to the case of the time-correlated function when £=100% . In Figs. 2(a)-2(c), the x-coordinate represents the phase variation of the electro-optic modulator 8, and the y-coordinate represents the recorded coincidence count.
If the memory-based beam splitter M-BS2 is inserted (for £=100%), the two arms of the interferometer are recombined and a wave-like phenomenon sketched in the red curve is observed.
While the memory-based beam splitter M-BS2 is removed (£ = 0), corresponding to the situation that the leaked part is not converted to the spin wave and passes through the third two-dimensional magneto-optical trap 1c directly, the interferometer remains open, and hence, no interference is observed, which reveals the particle-like nature, as shown in the red curve.
/ 25 LU102075 In Figs. 2(a)-2(c), the coincidence counts are recorded against the phase of the electro-optic modulator 8 with a step of 7/4. The red curves are fitted by: N] EIT, + Je PAF] N is the total photon counts, and N = 650+10, 7, =0.151+0.002 , Moon =0.87410.011, 7, =0.247£0.005. The fitted £ obtained from Figs. 2(a)-2(c) is 0.001, 0.530, 0.960, respectively. Fig. 2(d) shows the simulated result of the wave-like behavior, the particle-like behavior and intermediate situations when N = | 650, 7, =0.151, n,,=0.874,and 7, =0.247.
In the present invention, by changing the relative proportion (£= 0, 50%, 1) of the QRNG, the wave-like behavior, the particle-like behavior and intermediate states between them are further revealed. Usually, the quantum delayed-choice experiment needs the assistance of a superposition state prepared, and then measurement is performed by inserting or removing the memory-based beam splitter, and the wave-particle change is observed. In the solution of the present invention, the assistant can be described by a density operator p. In Fig. 2, & takes different values, and a phenomenon from particle to wave is observed in the present invention. In the Mach-Zender interferometer as depicted in Fig. 2(c), the calculated visibility of interference is not very high due to the mismatching of two retrieval signals, which is mainly caused by the different bandwidths of two memories. In Fig. 2(a), the interference disappears, revealing the particle-like nature of photons. Moreover, in the present invention, it is investigated that the intermediate situation between the wave-like behavior and the particle-like behavior, as described in Fig. 2(b), which reveals the changes between the wave-like behavior and the particle-like behavior. Besides, as shown in Fig. 2(d), the wave-like behavior, the particle-like behavior and intermediate situations between them are simulated in the preset invention by using experimental parameters to further illustrate the Wheeler’s delayed-choice experiment. All the results elucidate that the observed behavior of photons is intrinsically dependent on the detection device.
16 / 25 LU102075 Embodiment 2 The demonstration apparatus of the present invention can further describe the wave particle characteristics by adjusting the relationship between the interference ability of the interferometer and the storage parameters (e.g., storage efficiency and storage time) and by observing whether the interference is produced or not, so as to further observe and prove the wave-particle complementarity in the in light-matter ; interaction. | As shown in Fig. 3, the storage efficiency in the third two-dimensional magneto-optical trap lc is changed by varying the Rabi frequency of the second coupling light beam 7b from 2x x 27.86 to 0, and the visibility of interference is varied against different storage efficiencies. In Fig. 3(a)-3(e), the x-coordinate represents the phase variation of the electro-optic modulator 8, and the y-coordinate represents the recorded coincidence count. The red curves are fitted by: N JT hn V2 + me” P (where, N = 568440, n, = 0.122+0.011, Ton =
0.850). The 7,= 0.331, 0.259, 0.114, 0.015, 0 for Figs. 3(a)-3(e), respectively. Fig. 3(f) is the simulated interference as a function of the effective storage efficiency of the third two-dimensional magneto-optical trap lc, reflecting the simulated interference ability of the interferometer with the change of 7, (N = 568, n, =
0.122, Men = 0.850). As shown in Fig. 3 (a), the maximum visibility corresponds to the storage efficiency of 33.1% in the third two-dimensional magneto-optical trap 1c. Here, to obtain perfect interference, according to the present invention, the retrieval signals after two storage processes are balanced. In this regard, according to the present invention, a suitable storage efficiency of the spin wave in the third two-dimensional magneto-optical trap 1c is chosen by varying the Rabi frequency of the second coupling light beam 7b. Aside from this, it is also crucial to the choose a suitable storage efficiency in the second two-dimensional magneto-optical trap 1b. Because if the storage efficiency in the second two-dimensional magneto-optical trap : 1b is too large, the leaked part as the input of the second storage process is too little to
17 / 25 LU102075 obtain the enough retrieval signal after the third two-dimensional magneto-optical trap 1c. Since the Raman storage efficiency is significantly dependent on the optical depth of the atomic ensemble, a controllable leaked component of single photon could be controlled by changing the optical depth of the atomic ensemble. As a result, in the experiment of the present invention, the storage efficiencies in the second two-dimensional magneto-optical trap 1bandthe third two-dimensional magneto-optical trap 1c are optimized to achieve the best interference. As shown in Fig. 3(e), the minimum visibility corresponds to the storage efficiency of 0 in the third two-dimensional magneto-optical trap 1c, suggesting the particle behavior.
Embodiment 3 The demonstration apparatus of the present invention can further observe the character change form wave to particle by varying the storage time of the spin wave in the third two-dimensional magneto-optical trap 1c.
Fig. 4 shows a demonstration where the quantum memory acts as a temporal beam splitter. Fig. 4 (a)-4(f) reflects the interference pattern with the different storage time of the spin wave in the third two-dimensional magneto-optical trap 1c from T =160ns to 280 ns. In Fig. 4 (a)-4(f), the x-coordinate represents the phase variation of the electro-optic modulator 8, and the y-coordinate represents the recorded coincidence count. Dots are experimental data, and red curves are a sine function or a constant function. The best interference pattern is shown in Fig. 4(c) with the storage time of 200 ns, which is identical to the storage time in the second two-dimensional magneto-optical trap 1b. Intrinsically, the visibility of interference is positively correlated to the degree of overlap between two retrieval signals. When the storage time of the spin wave in the third two-dimensional magneto-optical trap 1c is varied, the degree of temporal overlap between two parts of the first optical signal 2a is also changing. There is no interference pattern in Fig. 4(a) and Fig. 4(f) with the storage time of 160ns or 280 ns, in which the two retrieval signals are almost separated. The overlap time window is about 120 ns (=280-160 ns), which is closed to the coherence time (110 ns) of the retrieved optical mode. In addition, the degree of overlap between two retrieval signals can also be controlled by adjusting the waveforms or bandwidth of two retrieval wave packets. In the solution of the present invention, the wave-particle complementarity is studied by varying the storage time of the spin wave in the third two-dimensional magneto-optical trap lc, so as to observe the character change form wave to particle. With the aid of this flexible and controllable temporal Mach-Zender interferometer, the obtained results are in favor of our comprehension of Bohr’s complementarity principle in light-matter interaction.
In the present invention, the repetition rate of the experiment is 100 Hz, the corresponding period of each experiment is 10ms, and the trapping time (i.e., the preparation time of cold atoms) of the two-dimensional magneto-optical trap is 8.7 ms. Moreover, the experimental window (the blank time of the experiment, i.e., the time interval between the completion of data collection after a complete experimental period and the start of the next experiment) is 1.3 ms. The time of the experiment is controlled by the switching of the light path implemented by the acousto-optic modulator.
The demonstration apparatus and demonstration method of the present invention verify the Wheeler’s delayed-choice experiment with a temporal Mach-Zender interferometer consisting of the Raman memory-based beam splitters (M-BS) of two atomic atomic ensembles and a 200-m optical fiber. By changing the relative | proportion of M-BS, the storage efficiency, the storage time and other experimental | parameters, the wave-like behavior, the particle-like behavior as well as intermediate states between them are observed. The resulting Wheeler’s delayed-choice experiment under light-atom interaction gives a fundamental aspect that it makes no sense to illustrate the wave-like or particle-like behavior of light and matter before the measurement happens.This experimental apparatus can not only be used as an experimental teaching apparatus in the classroom, but also pave the way for | implementing foundational-like tests and applications of quantum mechanics in the macroscopic interface of light-atom interaction.
The above specific embodiments cannot be regarded as a limitation to the scope of protection of the present invention. For those skilled in the art, any alternative improvement or modification made to the embodiments of the present invention shall
19 / 25 LU102075 fall within the scope of protection of the present invention.
What is not described in detail in the present invention is the well-known technology in the technical field for those skilled in the art.
Claims (9)
1. À temporal Wheeler’s delayed-choice demonstration apparatus, comprising: a first two-dimensional magneto-optical trap (la), wherein, the first two-dimensional magneto-optical trap (1a) is configured to generate a Stokes photon and an anti-Stokes photon in a spontaneously four-wave mixing process; the Stokes photon is a first optical signal (2a), and the anti-Stokes photon is a second optical signal (2b); the first optical signal (2a) and the second optical signal (2b) are counter transmitted out of the first two-dimensional magneto-optical trap (1a); the second optical signal (2b) is collected into a second single-photon counting module (4b) to be detected through a first convex lens (3a); the first optical signal (2a) is coupled into a first single-mode optical fiber (5a) through a second convex lens (3b); a first pump light (6a) and a second pump light (6b) are orthogonal polarization, propagate counter collinearly, and are transmitted into the first two-dimensional magneto-optical trap (1a) to generate the spontaneously four-wave mixing process; a small angle is formed between the first pump light (6a) and the second optical signal (2b), and a small angle is formed between the second pump light (6b) and the first optical signal (2a); a second two-dimensional magneto-optical trap (1b), wherein, after being transmitted by the first single-mode optical fiber (5a), the first optical signal (2a) passes through a third convex lens (3c), first enters the second two-dimensional : magneto-optical trap (1b), is then transmitted out of the second two-dimensional ; magneto-optical trap (1b), and is coupled to a second single-mode optical fiber (Sb) through a fourth convex lens (3d); ' a first coupling light beam (7a) is transmitted into the second two-dimensional ; magneto-optical trap (1b) to adjust a storage time of the first optical signal (2a) in the second two-dimensional magneto-optical trap (1b); a third two-dimensional magneto-optical trap (lc); wherein, after being transmitted by the second single-mode optical fiber (5b), the first optical signal (2a) passes through a fifth convex lens (3e), first enters the third two-dimensional _
magneto-optical trap (lc), is then transmitted out of the third two-dimensional magneto-optical trap (1c), and is collected into a first single-photon counting module (4a) to be detected through a sixth convex lens (31); a second coupling light beam (7b) is transmitted into the third two-dimensional | magneto-optical trap (1c) to adjust a storage time of the first optical signal (2a) in the third two-dimensional magneto-optical trap (1c); an electro-optic modulator 8, wherein, the electro-optic modulator 8 is connected in the second single-mode optical fiber (5b); the electro-optic modulator 8 is configured to introduce a phase shift for the first optical signal (2a) when the first optical signal (2a) is transmitted in the second single-mode optical fiber (5b); and an alkali metal atomic ensemble is trapped in each of the first two-dimensional magneto-optical trap (1a), the second two-dimensional magneto-optical trap (1b) and the third two-dimensional magneto-optical trap (1c); the alkali metal atomic ensemble in the first two-dimensional magneto-optical trap (la) is used to generate a heralded single photon; the alkali metal atomic ensemble in the second two-dimensional magneto-optical trap (1b) and the alkali metal atomic ensemble in the third two-dimensional magneto-optical trap (1c) are used as memory-based beam splitters.
2. The demonstration apparatus of claim 1, wherein, switching of the first pump light (6a) and switching of the second pump light (6b) are confrolled by a first acousto-optic modulator (9a) and a second acousto-optic modulator (9b), respectively; switching of the first coupling light (7a) and switching of the second coupling light (7b) are controlled by a third acousto-optic modulator (9c) and a fourth acousto-optic modulator (9d), respectively; all the acousto-optic modulators are modulated by an arbitrary function generator, respectively.
3. The demonstration apparatus of claim 1, wherein, an optical depth of the first two-dimensional magneto-optical trap (la) is 40, an optical depth of the second two-dimensional magneto-optical trap (1b) is 35, and an optical depth of the third | two-dimensional magneto-optical trap (1c) is adjusted between 0 and 40.
22 / 25 LU102075
4. The demonstration apparatus of claim 1, wherein, each of a length of the first single-mode optical fiber (5a) and a length of the second single-mode optical fiber (5b) is preferably 200-250 meters.
5. The demonstration apparatus of claim 1, wherein, the alkali metal atomic ensemble is a rubidium atomic ensemble or a cesium atomic ensemble.
6. A demonstration method for verifying a wave-particle complementarity of light using the demonstration apparatus of any one of claims 1-5, comprising the following steps: step 1: controlling switching of a first pump light (6a) and switching of a second pump light (6b) by a first acousto-optic modulator (9a) and a second acousto-optic | modulator (9b), respectively; wherein the first pump light (6a) and the second pump | light (6b) of orthogonal polarization propagate counter collinearly into a first two-dimensional magneto-optical trap (1a) to generate a spontaneously four-wave mixing process; generating a Stokes photon and an anti-Stokes photon by the first two-dimensional magneto-optical trap (la) in the spontaneously four-wave mixing process, wherein the Stokes photon is a first optical signal (2a), the anti-Stokes photon is a second optical signal (2b), and the first optical signal (2a) and the second optical signal (2b) are counter transmitted out of the first two-dimensional magneto-optical trap (1a); wherein a small angle is formed between the first pump light (6a) and the second optical signal (2b), and a small angle is formed between the second pump light | (6b) and the first optical signal (2a); collecting the second optical signal (2b) into a | second single-photon counting module (4b) through a first convex lens (3a), and ; coupling the first optical signal (2a) into a first single-mode optical fiber (5a) through a second convex lens (3b); step 2: making the first optical signal (2a) from the first single-mode optical fiber | (5a) pass through a third convex lens (3c) and then enter a second two-dimensional | magneto-optical trap (1b), and adiabatically switching off a first coupling light beam (7a), wherein the first optical signal (2a) is stored in the second two-dimensional magneto-optical trap (1b); afier a programmable storage time, switching on the first coupling light beam (7a) again, wherein the first optical signal (2a) is released from
| 23 / 25 LU102075 the second two-dimensional magneto-optical trap 1b, and meanwhile, the first optical signal (2a) is divided into a stored part and a leaked part in time domain, and the stored part and the leaked part constitute two arms of a temporal Mach-Zender | interferometer, respectively; step 3: making the first optical signal (2a) from the second two-dimensional magneto-optical trap (1b) coupled into a second single-mode optical fiber (5b) through a fourth convex lens (3d) to generate an optical delay; when the first optical signal (2a) is transmitted in the second single-mode optical fiber (5b), generating a phase shift on the stored part by an electro-optic modulator (8); | step 4: making the first optical signal (2a) transmitted from the second single-mode optical fiber (5b) pass through a fifth convex lens (3e) and then enter a third two-dimensional magneto-optical trap (1¢); controlling switching of the second coupling light beam (7b) by a fourth acousto-optic modulator (9d) to control insertion or removal of the third two-dimensional magneto-optical trap (1c) as a memory-based beam splitter in the experimental apparatus; step 5: collecting the first optical signal (2a) from the third two-dimensional magneto-optical trap (1c) into a first single-photon counting module (4a) through a sixth convex lens (3); and step 6: sending an electrical signal from the second single-photon counting module (4b) and an electrical signal from the first single-photon counting module (4a) to a time-correlated single-photon counting system to measure a corresponding time-correlated function. |
7. The demonstration method of claim 6, wherein, in step 4, a relative proportion of a quantum random number generator can be varied to adjust a degree of the insertion of the third two-dimensional magneto-optical trap (1c) as the memory-based beam splitter in the experimental apparatus, so as to observe a change of a wave-particle behavior through a change of an interference intensity.
8. The demonstration method of claim 6, wherein, in step 4, a Rabi frequency of >"
| 24 / 25 | LU102075 the second coupling light beam (7b) can be varied to adjust a storage efficiency of the third two-dimensional magneto-optical trap (lc), so as to observe a change of a wave-particle behavior through a change of an interference intensity.
9. The demonstration method of claim 6, wherein, in step 4, a storage time of the third two-dimensional magneto-optical trap (1c) can be varied, so as to observe a change of a wave-particle behavior through a change of an interference intensity.
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