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Energy level diagram and experimental arrangements. (a) Energy level of D 2-line transition of 87 Rb for EIT-based backward FWM. All fields are on resonance. (b) Schematic of the experimental setup. DL, diode laser; AOM, acousto-optic modulator; SMF, single-mode fiber; POL, polarizer; PBS, polarization beam splitter; HWP, half-wave plate; QWP, quarter-wave plate; L, lens; FM, flipping mirror; P, pinhole; PMT, photo-multiplier tube. (c) Relative-propagating direction arrangement of the optical beams. A small angle of approximately 0.4° is set between the probe and coupling beams. The driving beam is exactly counter propagating and coincides with the probe beam. The generated signal field is in the opposite direction of the coupling field, according to phase-match condition.
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Electromagnetically-induced-transparency-based four-wave mixing (FWM) in a resonant four-level double-Λ system has a maximum conversion efficiency (CE) of 25% due to spontaneous emission. Herein, we demonstrate that spontaneous emission can be considerably suppressed by arranging the applied laser beams in a backward configuration. With the backwar...
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... Details. In the present study, we conduct the backward FWM experiment in a laser-cooled 87 Rb atomic system. The relative energy levels and optical fields are shown in Fig. 1(a). All the cold atoms are ini- tially prepared in the ground state | 〉 1 by optical pumping. A weak probe field (Ω p denotes its Rabi frequency) is on a resonance of | 〉 ↔ | 〉 1 3 transition and forms a standard Λ-type EIT system with a strong coupling field (Ω c ), which drives | 〉 ↔ | 〉 2 3 transition. A driving field (Ω d ) drives | 〉 ...
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... experimental setup is shown in Fig. 1(b). The probe field is produced from the diode laser (DL1), and the coupling and driving fields are generated by another diode laser (DL2). DL2 is directly injection locked by an external cavity diode laser, whereas DL1 is injection locked by an intermediate laser that is injection locked using the same external cavity diode laser through ...
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... propagation direction and the relative position of the applied optical beams are depicted in Fig. 1(c). The coupling and probe beams are separated by a small angle of approximately 0.4° to reduce the light leakage from the coupling field. To conduct the backward FWM experiment, the driving field propagates from the opposite side of the cold atomic medium and is made to coincide with the probe field. Due to the phase-match condition, ...
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... to reduce the light leakage from the coupling field. To conduct the backward FWM experiment, the driving field propagates from the opposite side of the cold atomic medium and is made to coincide with the probe field. Due to the phase-match condition, the propagation direction of the FWM signal field is the opposite of that of the coupling field [ Fig. 1(c)]. The probe and signal pulses are detected by a photomultiplier tube module, and then recorded by an oscilloscope. The overall detection efficiencies for the probe and signal fields are approximately 25% and 10%, respectively, in the backward FWM ...
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... that to satisfy the condition that the spectral width of the probe pulse is much smaller than the width of the EIT transparency window, we set the duration of the probe square pulse to 40 μs. Theoretical Model. We consider a four-level atomic system with two ground states (| 〉 1 and | 〉 2 ) and two excited states (| 〉 3 and | 〉 4 ), as shown in Fig. 1(a). The behavior of probe and signal pulses in the atomic medium under the backward FWM process are described by the Maxwell-Schrödinger equations (MSEs) as follows: when the degenerate Zeeman sublevels are considered. The minus sign of the space-derivative term in equation (2) indicates that the propagation direction of the signal pulse ...
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... We have discussed a theoretical model for the EIT-based backward FWM under ideal conditions. However, experiments usually involve some unwanted effects. In our experiment, the phase-mismatch effect cannot be neglected and should be included in the theoretical model. In our backward double-Λ scheme, the phase-mismatch term is expressed as follows: Fig. 1(c). If the phase-mismatch term, ∆k, is zero, the generated signal field in the backward FWM can be obtained from equation (11). However, if ∆ ≠ k 0, the phase-mismatch effect should be considered in the theoretical model. To include the phase-mismatch effect in the backward FWM, we can change the variable of Ω = Ω′ ∆ e s s i ...
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... of the driving field and measure the variation of CE in back- ward FWM processes, where the parameters of Ω d are 0.10Γ, 0.25Γ, 0.37Γ, and 0.45Γ in Fig. 3(a-d), respectively. The phase-mismatch term ∆k is calculated to be approximately 0.091 π mm / according to the propagating direc- tions of the probe, coupling, and driving fields mentioned in Fig. 1(c). Because the size of the cold atomic cloud . According the theoretical curves, the steady-state CEs of the incident probe to the FWM signal are 6%, 36%, 53%, and 49% in (a-d), respectively. in the MOT is measured to be approximately 4 mm, the value of ∆kL is determined to be 0.364π in the experi- ment shown in Fig. 3. According to the ...
Citations
... Many theoretical and experimental studies have been performed to demonstrate the FWM process in atomic system. Four level N-type [15][16][17][18], Y-type [19], double Λ-type [20][21][22], diamond-type [23][24][25][26][27] atomic systems become very popular for the investigation of FWM process. In a four level atomic system, three electromagnetic fields of frequencies ω 1 , ω 2 , ω 3 nonlinearly interact with the atoms and generate FWM signal which has a frequency ω g = ± ω 1 ± ω 2 ± ω 3 . ...
... In absence of MW field, the efficiency of the FWM process (η eff ) is 5.36%. Note that FWM generation also depends on the intensities of the control fields |Ω c | 2 , |Ω q | 2 as shown in equation (18) and can be enhanced further by adjusting the control fields. ...
We theoretically investigate a N-type ⁸⁷Rb atomic system for efficient generation and control of a non-degenerate four wave mixing (FWM) signal in pulsed regime. The susceptibility of the atomic medium is customized as a gain profile by a weak probe pulse and two strong continuous wave control fields which allow us to generate the pulsed FWM signal. We study the propagation dynamics of the generated FWM signal inside the nonlinear medium. The FWM signal obtains the exact shape of the probe pulse and travels without changing the shape whereas, the probe pulse is absorbed inside the nonlinear medium. The conversion efficiency of this scheme without a MW field is 5.36%. However, a MW field that couples two metastable ground states enhances the conversion efficiency to 20.6%. The generation and control of such FWM signal in pulsed regime has important applications in signal processing, optical communication and information science.
... Many theoretical and experimental studies have been performed to demonstrate the FWM process in atomic system. Four level Ntype [8][9][10][11], Y-type [12], double Λ-type [13,14], diamond-type [15][16][17][18][19] atomic systems become very popular for the investigation of FWM process. In a four level atomic system, three electromagnetic fields of frequency ω 1 , ω 2 , ω 3 nonlinearly interact with the atoms and generate FWM signal which has a frequency ω g = ±ω 1 ± ω 2 ± ω 3 . ...
... They observe FWM conversion efficiency of 3.8% when control laser intensity is low and 46% when control laser intensity is high. Note that FWM conversion efficiency can be enhanced considerably by increasing the control field intensity and optical depth of the medium [11,[25][26][27]. Along with the improvement of FWM conversion efficiency, the shape of the generated FWM signal at medium output becomes equally important. ...
We theoretically investigate a N-type atomic system for efficient generation and control of a non-degenerate Four wave mixing (FWM) signal. The susceptibility of the atomic medium is customized as a gain profile by a weak probe field and two strong control fields which allow us to generate the FWM signal. We study the propagation dynamics of the generated FWM signal inside the nonlinear medium. The FWM signal obtains the exact shape of probe pulse and travels through the atomic medium without changing the shape. The conversion efficiency without MW field is 5.8% which can be enhanced further by changing the control field intensity and optical depth. We also demonstrate how the FWM conversion efficiency can be enhanced three times using a MW field. The generation and control of such FWM signal has important applications in signal processing, optical communication and quantum information science.
... (25) and (26)]. This system is also known as an open-loop FWM system and can be used as an efficient frequency converter [40][41][42][43][44]. ...
Hong-Ou-Mandel (HOM) interference is a compelling quantum phenomenon that demonstrates the nonclassical nature of single photons. Herein, we investigate an electromagnetically induced transparency-based double-Lambda four-wave mixing system from the perspective of quantized light fields. The system can be used to realize efficient HOM interference in the frequency domain. By using the reduced density operator theory, we demonstrate that, although the double-Lambda medium does not exhibit phase-dependent properties for the closed-loop case of two incident single photons, frequency-domain HOM two-photon interference occurs. For experimentally achievable optical depth conditions, our theory indicates that this double-Lambda scheme can perform high-fidelity Hadamard gate operations on frequency-encoded single-photon qubits, and thereby generate HOM two-photon NOON states with a fidelity greater than 0.99. Furthermore, we demonstrate that this scheme can be used to realize arbitrary single-qubit gates and two-qubit SWAP gates by simply controlling the laser detuning and phase, exhibiting its multifunctional properties and providing a new route to scalable optical quantum computing.
... Another promising approach for implementing low-loss frequency converters is the use of a resonant FWM system based on electromagnetically induced transparency (EIT) [14][15][16][17][18]. Because EIT can greatly enhance nonlinear interactions between photons and considerably suppress vacuum field noise under ideal conditions, many EIT-based quantum applications have been proposed and demonstrated at the single-photon level; these applications include quantum memory [19][20][21], photonic transistors [22][23][24], optical phase gates [25][26][27], and frequency beam splitters [28]. ...
... To obtain such a high CE, effective suppression of the spontaneous emission loss in this resonant-type FWM system is essential. A simple solution involves backward configuration of the applied laser fields [15,17]. However, the phase mismatch due to the backward configuration can cause significant decreases in CE. ...
... The experimental data in Fig. 3(b) show that at a two-photon detuning setting of −27 kHz, the maximum CE can reach 91.2% ± 0.6%. Moreover, the bandwidth of this resonant backward FWM is approximately 0.8 MHz, which is mainly affected by the EIT effect and the intensity balance condition [17], so the bandwidth can be increased by increasing the intensity of the coupling and driving light. The experimental observations of the resonant backward FWM in the pulsed regime can be found in Supplement 1. ...
Efficient frequency conversion of photons has important applications in optical quantum technology because the frequency range suitable for photon manipulation and communication usually varies widely. Recently, an efficient frequency conversion system using a double- $\Lambda$ Λ four-wave mixing (FWM) process based on electromagnetically induced transparency (EIT) has attracted considerable attention because of its potential to achieve a nearly 100% conversion efficiency (CE). To obtain such a high CE, the spontaneous emission loss in this resonant-type FWM system must be suppressed considerably. A simple solution is to arrange the applied laser fields in a backward configuration. However, the phase mismatch due to this configuration can cause a significant decrease in CE. Here, we demonstrate that the phase mismatch can be effectively compensated by introducing the phase shift obtained by two-photon detuning. Under optimal conditions, we observe a wavelength conversion from 780 to 795 nm with a maximum CE of $91.2\% \pm 0.6\%$ 91.2 % ± 0.6 % by using this backward FWM system at an optical depth of 130 in cold $^{87}{\text{Rb}}$ 87 Rb atoms. The current work represents an important step toward achieving low-loss, high-fidelity quantum frequency conversion based on EIT.
... Most of these works suffered large insertion loss induced by media, which not only reduces the output-to-input ratio but also may lead to additional quantum noise. Here, our low-loss FBS is made with the four-wave mixing (FWM) process based on the double-electromagnetically induced transparency (EIT) scheme [26][27][28][29][30][31][32][33]. Using the transition scheme depicted in Fig. 1(a), we converted a coherent-state single photon in the 780-nm mode to another photon in the superposition of 780-and 795-nm modes, and demonstrated that the 50/50 FBS has an output-to-input ratio of 90 ± 4%. ...
A frequency beam splitter (FBS) with the split ratio of 0.5, i.e., 50/50 FBS, can be used as the frequency-mode Hadamard gate for frequency-encoded photonic qubits. A FBS with the split ratio of 1 is exactly the coherent frequency converter (CFC) for frequency up or down conversion of photons. Previous works revealed that all kinds of 50/50 FBS and CFC operating at the single-photon level had overall efficiency or output-to-input ratio around 50% or less. In this work, our 50/50 FBS and CFC are made with the four-wave mixing (FWM) process based on the double-Λ electromagnetically induced transparency (EIT) scheme. We achieved an overall efficiency of 90 ± 4% in the 50/50 FBS and that of 84 ± 4% in the CFC using coherent-state single photons, both of which are the best up-to-date records. Furthermore, we utilize the scheme of Hong-Ou-Mandel interference (HOMI) to measure the fidelity or degree of coherence of the FBS. The fidelity indicated by the HOMI's g(2) measurement of the 50/50 FBS is 0.99 ± 0.01. This high fidelity demonstrates the low noise of the frequency conversion in the EIT-based FWM process. Such low-loss high-fidelity FBS with the tunable split ratio can lead to useful operations or devices in long-distance quantum communication.
... One such example is an atom, whose energy levels are placed under the influence of the standing wave fields in a subwavelength domain. This new technique has enabled us to witness some basic phenomena, which among many include electromagnetically induced absorption [18,19], population trapping [20,21], superluminal and subluminal propagation of light [22][23][24][25][26], Kerr nonlinearity [27,28], optical bistability [29,30], four-wave mixing [31,32], electromagnetically induced transparency [33,34] and optical multistability [35,36]. Atom localization phenomena are also investigated by calculating the optical Bloch equations based on the formalism of the density matrix. ...
We have theoretically investigated two-dimensional atom localization using the absorption spectra of birefringence beams of light in a single wavelength domain. The atom localization is controlled and modified through tunneling effect in a conductive chiral atomic medium with absorption spectra of birefringent beams. The significant localization peaks are investigated in the left and right circularly polarized beam. Single and double localized peaks are observed in different quadrants with minimum uncertainty and significant probability. The localized probability is modified by controlling birefringence and tunneling conditions. These results may be useful for the capability of optical microscopy and atom imaging.
... The double-atom-light coupling scheme finds a wide range of applications, including light storage [3,4], generation of squeezed light states [5,6], phase-controlled light switching [7,8], frequency conversion [9][10][11][12][13][14][15][16][17], and orbital angular momentum conversion [18][19][20][21] between light beams, as well as many others [2,[22][23][24][25][26][27]. In most of these works, two configurations of the applied laser fields are usually encountered. ...
We show that for the two widely used configurations of the double- $\Lambda$ Λ atom–light coupling scheme, one where the control fields are applied in the same $\Lambda$ Λ -subsystem and another where they are applied in different $\Lambda$ Λ -subsystems, the forward propagation of the probe and signal fields is described by the same set of equations. We then use optimal control theory to find the spatially dependent optimal control fields that maximize the conversion efficiency from the probe to the signal field, for a given optical density. This work can find application in the implementation of efficient frequency and orbital angular momentum conversion devices for quantum information processing, as well as to be useful for many other applications using the double- $\Lambda$ Λ atom–light coupling scheme.
... In the FWM process, three electromagnetic fields interact in a nonlinear optical system and generate an electromagnetic field with a new frequency. Numerous experiments have been carried out to demonstrate the enhanced FWM process in multi-level atomic systems [24][25][26][27][28][29]. The FWM process using EIT has been observed in both cold [30,31,[26][27][28][29] and room-temperature [25,32] atomic systems. ...
... Numerous experiments have been carried out to demonstrate the enhanced FWM process in multi-level atomic systems [24][25][26][27][28][29]. The FWM process using EIT has been observed in both cold [30,31,[26][27][28][29] and room-temperature [25,32] atomic systems. Besides the FWM process, enhanced higherorder multi-wave mixing processes have been studied [33]. ...
We present an efficient scheme for the generation and control of a non-degenerate four-wave mixing (FWM) signal in a N -type inhomogeneously broadened 87 Rb atomic system. We observe the propagation dynamics of the generated FWM signal along with the probe pulse under the condition of Electromagnetically Induced Transparency (EIT). The FWM signal acquiring the scaled shape of probe field travels through the medium without changing its shape and intensity. We have also shown that a time dependent control field
permits the storage and retrieval of these optical signals without losing their identity. This work allows us to generate, control, store and retrieve FWM signal of complicated shape.
... The suppression and enhancement of four-wave-mixing (FWM) process in electromagnetically induced transparency (EIT) windows [1][2][3][4][5][6][7][8] can be implemented in many multi-level systems, such as ladder-type, [2,9,10] Y-type, [8] and double lambda-type [4][5][6][11][12][13] level configurations. In a ladder-type system with hyperfine ground states, the magnitude of FWM signal is found to be dependent on the transition route, and dominantly related to the residual two-photon coherence according to the degree of optical pumping to the other ground state. ...
... [8] Recently, in a backward double-lambda system, the conversion efficient in cold rubidium atoms was observed to be 63%, and the conversion efficient was predicted to be 96% by using a medium with a large optical depth. [13] The control of FWM process can be achieved by changing several parameters of the fields applied to the system, e.g., the detuning and the strengths, [8,14] the relative phases, [15] and the pulse dynamics. [16] This control of FWM process can be applied to the quantum entanglement, [17] the fabrication of scalable multimode quantum resources, [18] and the enhancement of bright-seeded SU(1,1) interferometer. ...
Four-wave-mixing (FWM) process is examined by using density matrix formalism in a periodically-driven atomic medium. Numerical result shows that FWM signals can be controlled by selecting different dynamic parameters of the probe field and strengths of the inner-dressing fields. It is also shown that the controllable FWM process is dominantly influenced by the evolution of atomic population difference and two-photon coherence. This dynamic and inner-dressing control of FWM is probably used for optimizing the optical nonlinear process and information processing.
... Most of these works suffered large insertion loss induced by media, which not only reduces the output-to-input ratio but also may lead to additional quantum noise. Here, our low-loss FBS is made with the four-wave mixing (FWM) process based on the dual-Λ electromagnetically induced transparency (EIT) scheme [17][18][19][20][21][22][23][24]. Using the * yu@phys.nthu.edu.tw; ...
Frequency-encoded photonic qubits are not only more stable over long transmission distances but also more robust against birefringent materials. A 50/50 frequency beam splitter (FBS) is the Hadamard gate in quantum logic operation, which coherently converts a photon in one frequency or wavelength mode to another photon in the superposition of two different modes. Previous works revealed that the Hadamard gates or FBS's operating at the single-photon level had overall efficiencies or output-to-input ratios less than 50%. Here, our FBS is made with the four-wave mixing (FWM) process based on the dual-$\Lambda$ electromagnetically induced transparency (EIT) scheme. We achieved an overall efficiency of 90$\pm$4% with coherent-state single photons, which is the best up-to-date record for 50/50 FBS. In addition, we utilized this EIT-based scheme to perform wavelength conversion with light pulses of photon number less than one. We obtained an output-to-input ratio of 84$\pm$4%, which is not only the highest record currently achieved, but also the first experimental demonstration of preservation of the quantum state in the dual-$\Lambda$ EIT scheme. This demonstration was revealed by the fidelity of our Hadamard gate. To measure the fidelity, we propose a novel method using Hong-Ou-Mandel interference (HOMI) for quantum process tomography. The fidelity of our Hadamard gate indicated by the HOMI's $g^{(2)}$ measurement is 0.99$\pm$0.01. This low-loss high-fidelity Hadamard gate or wavelength converter based on the dual-$\Lambda$ EIT scheme can lead to useful operations or devices, such as entanglement swapping, multiplexer, etc., in long-distance quantum communication.
