A method of phononically controlled photonic routing

Abstract

The application discloses a method for phonon-controlled photonic routing, and belongs to the technical field of waveguide quantum electrodynamics. The method for phonon-controlled photonic routing is characterized in that a phonon microcavity and a giant atom are coupled to a double waveguide system, one of the waveguides is an infinite waveguide WN, the other waveguide is a semi-infinite waveguide WM, the giant atom is arranged in the phonon microcavity, the giant atom has one transition coupled to the photonic mode in the two waveguides, and the other transition is coupled to the phonon mode in the phonon microcavity. Compared with the prior art, the application introduces a giant atom and a phonon microcavity coupling model structure, so that the routing of non-resonant single photons can be effectively realized. Meanwhile, the infinite waveguide structure of the incident photons is changed into a semi-infinite waveguide by introducing a semi-infinite waveguide structure, so that the routing efficiency of single photons can be effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of waveguide quantum electrodynamics, and more specifically, relates to a method for phonon-controlled photon routing. Background Technology

[0002] The development of waveguide quantum electrodynamics (WQED) has spurred researchers to further explore the interaction between light and matter. These research results have important application value in quantum communication technology and quantum computing. One of the most representative research results is the invention of the single-photon router. Many theories and experiments on quantum routers have been carried out in various systems, including cavity quantum electrodynamic systems, optomechanical systems, and even purely linear optical systems.

[0003] Compared to other quantum systems, photons can serve as information carriers, enabling data distribution over longer distances in quantum tunnels. Therefore, single-photon routers have significant applications in quantum information processing. Superconducting qubits are one of the key schemes for realizing quantum information processing. As a method for building single-photon routers, researchers use superconducting qubits as "artificial atoms" and couple them to a one-dimensional transmission line, allowing microwave photons to travel along this line. By controlling the input frequency of the microwave photons, the artificial atoms can exhibit a non-interacting state with the photons, achieving electromagnetically induced transparency, thus ensuring that the incident photons are completely routed to the other end of the transmission line.

[0004] In 2014, experimental work demonstrated that superconducting qubits could be nonlocally coupled with one-dimensional waveguides. These superconducting qubits were termed "giant atoms." The superconducting qubits were coupled with surface acoustic waves (SAWs) propagating on a piezoelectric substrate, achieving the conversion between acoustic and electrical signals via interdigital transducers (IDTs). With further theoretical and experimental developments, the photon scattering properties of this system and their induced quantum optical effects have been extensively studied, leading to rapid research in quantum information processing devices such as single-photon frequency converters and routers. In recent years, to realize the single-photon multi-channel routing properties, a coupling model structure of giant atoms and two infinitely long transmission waveguides has also been investigated.

[0005] The core essence of the research on single-photon routers is to realize the coupling of two-level (multi-level) systems with multi-quantum channels. However, in the previous single-photon routers, there are three main problems: (1) photon routers based on giant atoms are only for specific frequencies; (2) the single-photon routing probability can only be changed by modulating the detuning frequency between the single photon and the giant atom; (3) the routing probability can only reach 0.5 under ideal conditions. Summary of the Invention

[0006] 1. The problem to be solved

[0007] The purpose of this invention is to provide a method for phonon-controlled photon routing to solve the above-mentioned technical problems of existing single-photon routers. The technical solution of this invention can achieve high-efficiency conversion of incident non-resonant photons, and under ideal conditions, the single-photon routing probability in a non-chiral coupling system can also reach 1.

[0008] 2. Technical Solution

[0009] To solve the above problems, the technical solution adopted by the present invention is as follows:

[0010] This invention provides a method for phonon-controlled photon routing, in which a phonon microcavity and a giant atom are coupled to a dual-waveguide system. One waveguide is an infinitely long waveguide WN, and the other waveguide is a semi-infinite waveguide WM. The giant atom is placed in the phonon microcavity, and one transition of the giant atom is coupled to the photon mode in both waveguides, while the other transition is coupled to the phonon mode of the phonon microcavity.

[0011] This invention couples a phonon microcavity to a giant atom into a dual-waveguide system, with one of the waveguides being an infinitely long waveguide WN. This enables efficient conversion of incident non-resonant photons. Furthermore, the routing probability of a single photon can be altered by adjusting the operating frequency of the phonon microcavity. Under ideal conditions, the routing probability of a single photon in the non-chiral coupling system can reach 1.

[0012] Furthermore, the giant atom has three energy levels: |e>, |s>, and |g>. The transition between the |e> and |s> levels is coupled through a phonon microcavity with a coupling strength of λ. The transition between the |e> and |g> levels is coupled through transmitted photons in waveguides WM and WN with a coupling strength of V. There is no coupling between the phonon microcavity and the waveguide.

[0013] Furthermore, the Hamiltonian of the model system is:

[0014] H = H f +H wa +H ra

[0015] Among them, Hf H is the free Hamiltonian for waveguides, giant atoms, and phonon microcavities. wa and H ra Let represent the Hamiltonians of the interactions between the waveguide and the giant atom, and between the phonon microcavity and the giant atom, respectively. Their specific expressions are as follows:

[0016]

[0017]

[0018]

[0019] In the above formula, i represents the imaginary unit; v g The group velocity of the photon motion; j = n, m represent waveguides WN and WM, respectively; Indicates the conjugate transpose symbol; c Rj (x) represents the generation and annihilation operators of photons propagating to the right in the waveguide, respectively. When j = n, they are the generation and annihilation operators of photons propagating to the right in the WN waveguide, and when j = m, they are the generation and annihilation operators of photons propagating to the right in the WM waveguide. c Lj (x) represents the generation and annihilation operators of photons propagating to the left in the waveguide, respectively. When j = n, these are the generation and annihilation operators of photons propagating to the left in the WN waveguide; when j = m, these are the generation and annihilation operators of photons propagating to the left in the WM waveguide. ω e and ω s ω represents the frequencies of energy levels |e> and |s>, respectively. c It is the operating frequency of the phonon microcavity; σ ee σ ss Let these represent the Pauli matrices corresponding to energy levels |e> and |s>, respectively. c corresponds to the generation and annihilation operators of the phonon cavity; δ(x) is the Dirac function; σ se , They represent the giant atomic energy levels respectively. The dipole transition descent and ascent operators; σ ge Represents giant atomic energy levels Hc is the dipole transition descent operator; Hc is the Hermitian conjugate operator.

[0020] Furthermore, the state function of the system is:

[0021]

[0022] In the above formula, φ RM (x), φ RN(x) represents the probability amplitude of a rightward-moving photon in waveguides WM and WN, respectively, and φ LM (x), φ LN (x) represents the probability amplitude of a photon moving to the left in waveguides WM and WN, respectively, u e u represents the probability amplitude of the giant atom being excited. s The amplitude representing the probability of a photon being present in the phonon microcavity, |0 w(c) > and |1 w(c) > indicates whether photons exist in the waveguide or resonant cavity, with 0 indicating no photons and 1 indicating photons. g, s, and e are the three energy levels of a giant atom.

[0023] Furthermore, the scattering probability amplitude of the system is as follows:

[0024]

[0025]

[0026]

[0027] Where, r m r is the reflection probability of a single photon in the waveguide WM. n and t n Δ represents the reflection probability and transmission probability of a photon after interacting with an atom and being routed into waveguide WN, respectively; ω =ω-ω c -ω s Δ e =ω-ω e This represents the detuning frequency resulting from the transition frequency between the incident photon and the giant atom energy level |e>→|g>. This represents the spontaneous emission rate of giant atoms. This represents the phase accumulation caused by the distance between different coupling points. This represents the phase accumulation caused by the distance between the coupling point and the waveguide terminal.

[0028] Furthermore, the single-photon reflection probability R in waveguide WM is defined. M =|r m | 2 The single-photon transmission probability T routed to waveguide WN N =|t n | 2 and reflection probability R N =|r n | 2 Under ideal conditions, the probability normalization relation is satisfied: |r m | 2 +|t n | 2 +|rn | 2 =1.

[0029] Furthermore, the giant atom is realized by superconducting qubits.

[0030] 3. Beneficial effects

[0031] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0032] (1) Compared with the prior art, this invention introduces a giant atom and phonon microcavity coupling model structure, which can effectively realize the routing of non-resonant single photons. At the same time, by introducing a semi-infinite waveguide structure, the infinitely long waveguide structure of the incident photon is changed into a semi-infinite waveguide, which can effectively improve the routing efficiency of single photons. When the reflection probability of the incident light is 0, the photon can be routed to the waveguide WN with unity efficiency.

[0033] (2) This invention introduces phonons to regulate the energy level transitions of giant atoms. That is, phonons generated in the microcavity control the transitions between the energy levels |s> and |e> of giant atoms. Therefore, by changing the operating frequency of the phonon microcavity, the detuning amount Δ between the phonon frequency and the energy level transition frequency of giant atoms can be further changed. ω This allows for the modification of the routing properties of single-photon scattering by adjusting the operating frequency of the phonon microcavity. Attached Figure Description

[0034] Figure 1 This is a system model structure diagram of the present invention.

[0035] Figure 2 This is a schematic diagram of the structure of a Λ-type giant atom three-level system;

[0036] Figure 3 The detuning Δ is the amount of time required to produce the transition frequency between the phonon microcavity frequency and the giant atom energy levels |e> and |s>. ω The curve showing the relationship between the scattering probability and the scattering probability;

[0037] Figure 4 Accumulated phase between coupling points At that time, phase factor A graph showing the relationship between the scattering probability and the scattering probability.

[0038] Figure 5 Accumulated phase between coupling points At that time, phase factor The curve showing the relationship between the scattering probability and the scattering probability. Detailed Implementation

[0039] like Figure 1As shown, this embodiment of the invention constructs a model structure of a giant atom coupled with a phonon microcavity and a dual waveguide. Waveguides WM and WN are two photon transmission channels; WM is a semi-infinite waveguide, and WN is an infinitely long waveguide. The central circle represents the giant atom, and the two sides of the giant atom are phonon microcavities (SAW resonators). The giant atom is placed within the SAW resonator. In this embodiment, the giant atom can be implemented using superconducting qubits, etc. Figure 2 The diagram shows a schematic of a Λ-type giant atom three-level system, which has three energy levels: |e>, |s>, and |g>. The transition between |e> and |s> is achieved through phonon microcavity coupling, where λ is the coupling strength. The transition between |e> and |g> is achieved through photon coupling via waveguides WM and WN. For waveguide WM, the coupling points are located at x = 0 and x = d. m1 At x = d, the coupling strength is V, and the waveguide is a semi-infinite waveguide. mt The coupling point is truncated at y = 0 and y = d. For a WN waveguide, the coupling point is located at y = 0 and y = d. n1 At each location, the coupling strength is V. There is no coupling between the phonon microcavity and the waveguide.

[0040] This invention also provides a method for phonon-controlled photon routing, employing the aforementioned model structure of a giant atom coupled with a phonon microcavity and a dual waveguide. Photons enter waveguide WM from the incident end, interact with the giant atom, and are finally routed to waveguide WN. The working principle is as follows:

[0041] The Hamiltonian describing the system is:

[0042] H = H f +H wa +H ra (1)

[0043] Among them, H f H is the free Hamiltonian for waveguides, atoms, and phonon microcavities. wa and H ra Let represent the Hamiltonians of the interactions between the waveguide and the atom, and between the resonant cavity and the atom, respectively. Their specific expressions are as follows:

[0044]

[0045]

[0046]

[0047] In the above formula, i represents the imaginary unit; v g The group velocity of the photon motion; j = n, m represent waveguides WN and WM, respectively; Indicates the conjugate transpose symbol; c Rj(x) represents the generation and annihilation operators for photons propagating to the right in the waveguide, respectively. c Lj (k) represent the generation and annihilation operators for photons propagating to the left in the waveguide, respectively; ω e and ω s ω represents the frequencies of energy levels |e> and |s>, respectively. c It is the operating frequency of the phonon microcavity; σ ee σ ss Let these represent the Pauli matrices corresponding to energy levels |e> and |s>, respectively. c corresponds to the generation and annihilation operators of the phonon cavity; δ(x) is the Dirac function; σ se , They represent the giant atomic energy levels respectively. The dipole transition descent and ascent operators; σ ge Represents giant atomic energy levels Hc is the dipole transition descent operator; Hc is the Hermitian conjugate operator.

[0048] The state function of the system can be described as:

[0049]

[0050] In the above formula, φ RM (x), φ RN (x) represents the probability amplitude of a rightward-moving photon in waveguides WM and WN, respectively, and φ LM (x), φ LN (x) represents the probability amplitude of a photon moving to the left in waveguides WM and WN, respectively, u e u represents the probability amplitude of the giant atom being excited. s The amplitude representing the probability of a photon being present in the phonon microcavity, |0 w(c) > and |1 w(c) > These represent whether photons exist in the waveguide or resonant cavity, with 0 indicating no photons and 1 indicating photons.

[0051] By solving the eigenvalue equation H|Ψ>=ω|Ψ>, the equation of motion for the system wave function is obtained as follows:

[0052]

[0053] Assuming that at the initial moment, a single photon is incident from the left end of waveguide WM, then the wave function of the single photon moving in the waveguide can be written as:

[0054]

[0055] In the above formula, r m and t mThe reflection and transmission probabilities of a single photon in a waveguide WM are r. n and t n Let a and b represent the reflection and transmission probabilities of a photon being routed into waveguide WN after interacting with an atom, respectively; a and b represent the single photon's x∈[0,d] in waveguide WM, respectively. m1 The probability amplitude of the region moving to the right or left; c represents the single photon in waveguide WM where x∈[d m1 ,d mt The probability amplitude of the region moving to the left; d and f represent the single photon's position in waveguide WN, x∈[0,d] n1 [x] The probability amplitude of the region moving to the right and left; H(x) is the Heaviside unit step function.

[0056] Substituting equation (5) into equation (4) and simplifying, we obtain the scattering probability amplitude of the system as follows:

[0057]

[0058]

[0059] Where, Δ ω =ω-ω c -ω s Δ e =ω-ω e This represents the detuning frequency resulting from the transition frequency between the incident photon and the giant atom energy level |e>→|g>. This represents the spontaneous emission rate of giant atoms. and These represent the phase accumulation caused by the distance between different coupling points and the distance between the coupling point and the waveguide terminal, respectively.

[0060] Under ideal conditions, the following relationship is satisfied: |r m | 2 +|t n | 2 +|r n | 2 =1, defining the single-photon reflection probability R in waveguide WM. M =|r m | 2 The single-photon transmission probability T routed to waveguide WN N =|t n | 2 and reflection probability R N =|r n | 2 .

[0061] The following example further illustrates how the present invention can alter the photon routing probability by adjusting the operating frequency of the phonon microcavity. Assume that at the initial moment, a single photon with a fixed frequency ω is incident from the left end of waveguide WM and interacts with the giant atom. The resulting single-photon scattering probability amplitude is shown in equation (6), and the result strongly depends on the single-photon incident frequency ω and the detuning frequency Δ. e With the operating frequency ω of the phonon microcavity c As shown in Figure (3), with a fixed giant atom size Under other parameters, by changing the operating frequency ω of the phonon microcavity c Detuning Δ ω =ω-ω c -ω s This will also change accordingly, thereby further achieving the effect of changing the probability of single photon scattering routes.

[0062] Meanwhile, compared to previous designs, single-photon routing always targets photons incident at their intrinsic frequency, or only achieves good routing performance when the incident photon resonates with an atom. The specific implementation scheme of this invention for achieving unit efficiency routing of non-resonant photons in a non-chiral coupling system is as follows. First, the operating frequency of the phonon microcavity is set to satisfy the relationship ω... c =ω e -ω s Then we have Δ ω =Δ e When a single photon is incident from the left end of waveguide WM, the scattering probability amplitude after interacting with the giant atom satisfies formula (6). According to the above calculations, under the incident condition of a non-resonant photon, when Δ... e When λ = kΓ (k is a positive integer), give two cases for achieving single photon routing to waveguide WN with unity efficiency:

[0063] (1) , where n is an integer.

[0064] (2) , where n is an integer.

[0065] That is, for a given giant atom size Phase accumulation at the coupling point and the boundary of the semi-infinite waveguide When the above conditions are met, the reflection probability R of a single photon in waveguide WM is... M =0,T N =R N =0.5, further realizing non-resonant single-photon routing from the WM waveguide to the WN waveguide with unity efficiency. As shown in Figures (4) and (5), when the phase factor is 0.5, When the values ​​of (1) and (2) above are taken, the incident photon is routed to the waveguide WN with unity efficiency, and the scattering probability TN ＝T R ＝0.5。

Claims

1. A method for phonon-controlled photon routing, characterized in that, Phononic microcavities and giant atoms are coupled to a dual-waveguide system. One waveguide is an infinitely long waveguide WN, and the other waveguide is a semi-infinite waveguide WM. The giant atom is placed in the phononic microcavity, and one transition of the giant atom is coupled to the photonic mode in both waveguides, and the other transition is coupled to the phononic mode of the phononic microcavity. Among them, giant atoms have three energy levels: , and ,in, and Transitions between energy levels are coupled through phonon microcavities. For its coupling strength, and Transitions between energy levels are coupled via transmitted photons in waveguides WM and WN, with coupling strengths of 1 and 2. The giant atom and the waveguide WM (WN) are coupled at points. and There is no coupling between the phonon microcavity and the waveguide; The Hamiltonian of the model system is: in, For waveguides, giant atoms, and phonon microcavities, the free Hamiltonian. and Let represent the Hamiltonians of the interactions between the waveguide and the giant atom, and between the phonon microcavity and the giant atom, respectively. Their specific expressions are as follows: In the above formula, Represents the imaginary unit; The group velocity of the photon's motion; These represent waveguides WN and WM, respectively. " indicates the conjugate transpose symbol; , These are the generation and annihilation operators for photons propagating to the right in the waveguide, respectively. , These are the generation and annihilation operators for photons propagating to the left in the waveguide, respectively. and They represent energy levels respectively. and frequency, It is the operating frequency of the phonon microcavity; , They represent energy levels respectively. and The corresponding Pauli matrix, , These correspond to the generation and annihilation operators of phonon microcavities; It is the Dirac function; , They represent the giant atomic energy levels respectively. The dipole transition descent and ascent operators; Represents giant atomic energy levels The dipole transition descent operator; It is the Hermitian conjugate operator.

2. The method for phonon-controlled photon routing according to claim 1, characterized in that, The state function of the system is: In the above formula, , These represent the probability amplitudes of rightward-moving photons in waveguides WM and WN, respectively. , These represent the probability amplitudes of photons moving to the left in waveguides WM and WN, respectively. This represents the probability amplitude of the giant atom being excited. u c This represents the probability amplitude of the presence of photons in the phonon microcavity. and These represent whether photons exist in the waveguide or resonant cavity, with 0 indicating no photons and 1 indicating photons.

3. The method for phonon-controlled photon routing according to claim 1 or 2, characterized in that, The scattering probability amplitude of the system is as follows: in, It is the reflection probability of a single photon in the waveguide WM. and These represent the reflection probability and transmission probability, respectively, of a photon after interacting with an atom and being routed into the waveguide WN. , Represents the energy levels of the incident photon and the giant atom. The detuning frequency generated by the transition frequency between them This represents the spontaneous emission rate of giant atoms. This represents the phase accumulation caused by the distance between different coupling points in waveguide WN or WM. This represents the phase accumulation in WM caused by the distance between the coupling point and the waveguide terminal.

4. The method for phonon-controlled photon routing according to claim 3, characterized in that, Define the single-photon reflection probability in a waveguide WM Single-photon transmission probability routed to waveguide WN and reflection probability .

5. The method for phonon-controlled photon routing according to any one of claims 1 or 2, characterized in that, The giant atom is realized by superconducting qubits.

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