Similar to their electronic counterpart, optical nonreciprocal devices play an important role and possess the fundamental function in photonic devices and quantum circuits, urging great research interest in an optical isolator[
Chinese Optics Letters, Volume. 20, Issue 1, 012701(2022)
Nonreciprocal transmission of multi-band optical signals in thermal atomic systems
Multi-band signal propagation and processing play an important role in quantum communications and quantum computing. In recent years, optical nonreciprocal devices such as an optical isolator and circulator are proposed via various configurations of atoms, metamaterials, nonlinear waveguides, etc. In this work, we investigate all-optical controlled nonreciprocity of multi-band optical signals in thermal atomic systems. Via introducing multiple strong coupling fields, nonreciprocal propagation of the probe field can happen at some separated frequency bands, which results from combination of the electromagnetically induced transparency (EIT) effect and atomic thermal motion. In the proposed configuration, the frequency shift resulting from atomic thermal motion takes converse effect on the probe field in the two opposite directions. In this way, the probe field can propagate almost transparently within some frequency bands of EIT windows in the opposite direction of the coupling fields. However, it is well blocked within the considered frequency region in the same direction of the coupling fields because of destruction of the EIT. Such selectable optical nonreciprocity and isolation for discrete signals may be greatly useful in controlling signal transmission and realizing selective optical isolation functions.
1. Introduction
Similar to their electronic counterpart, optical nonreciprocal devices play an important role and possess the fundamental function in photonic devices and quantum circuits, urging great research interest in an optical isolator[
The key to realize optical nonreciprocal devices is the nonreciprocal or asymmetric transmission of light. Magneto-optical materials were used to produce optical nonreciprocal propagation via the Faraday rotation effect[
Generally, random thermal motion of atoms has a negative impact on coherence of the quantum system, resulting in the decoherence effect or thermal noise[
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2. Model and Equations
We consider interaction of laser fields and the atomic system of levels, as shown in Fig. 1, in which the weak probe field and strong coupling fields couple corresponding energy levels in Fig. 1(a) and propagate along different directions, respectively, as shown in Figs. 1(b) and 1(c). The weak probe field of frequency couples states and , and the transitions are driven by the strong coupling fields of frequency , where and are corresponding half-Rabi frequencies of the fields with the electric dipole momentum and the electric field amplitudes and . The atomic gas is loaded in a cell, and its temperature is controlled by a temperature control system. In general, the atoms are in constant thermal motion following the Maxwell velocity distribution. Under the electric dipole and rotating-wave approximations, the Hamiltonian of the system can be written in the interaction picture as
Figure 1.Interaction of the laser fields and the multi-level atomic systems. (a) Laser coupling scheme, (b) co-propagation, and (c) counter-propagation setups of the probe field and the strong coupling fields.
Due to the irregular thermal motion, atoms in the hot atomic system move with various velocities in different directions. Under this condition, both frequencies of the lasers and frequency shift arising from the Doppler effect take effect on the interaction between lasers and atoms. Then, the detuning in Eq. (9) should be rewritten as with the atom of velocity and the wavevector of the laser . Assuming all the coupling lasers propagate along the same direction, the effective macro susceptibility for the probe field of co-/counter-propagation with the coupling lasers should be integrated on all the atoms of different velocities by
So, transmission of the probe field in the co-/counter-propagation direction can be regulated to pursue high asymmetric transmission in the two opposite directions by controlling the coupling fields.
3. Results and Discussion
Figure 2 shows transmissions of the co-propagating (red dash-dotted line) and the counter-propagating (blue solid line) probe fields in the three, four, five, and six-level atomic systems. In the calculation, we consider the atomic medium length , the atomic density , the temperature , and the other parameters are normalized by . It is clear that multiple nonreciprocal windows with separated frequency bands are generated in the multi-level atomic systems. When the probe field propagates along the opposite direction of the coupling fields, effects of the atom motion on the probe field and the coupling fields can be offset in the proposed configuration, which leads to the construction of the EIT under two-photon resonance and thus high transmissivity of the probe field in the EIT windows. Then, it can be seen that one or several separated high transmission bands (blue solid lines) are created in the transmission spectrum for the probe field, depending on the number and detuning of control fields. However, for the co-propagating probe field, frequency shifts induced by the atom motion produce remarkable two-photon detunings for the probe field and the coupling fields, which destruct the EIT effect and make large absorption of the probe field. Under this condition, the weak probe field interacts with an effective two-level atomic system, and probe photons are greatly absorbed by a large number of atoms. The following spontaneous emission can never generate a field along the incident direction of the probe field. Transmission of the co-propagating probe field is almost vanishing (red dashed-dotted lines) in a wide spectrum range. Therefore, multi-band nonreciprocal propagation of the probe field can be achieved in this atomic system by introducing multiple coupling lasers driving corresponding transitions.
Figure 2.Transmission of the probe field in multi-level atomic systems as a function of the probe detuning Δp, where the blue solid line stands for the counter-propagation and the red dash-dotted line for co-propagation. (a) Three-level system with Δ1 = 0, Ω1 = 40γ; (b) four-level system with Δ1 = −20γ, Δ2 = 20γ, Ω1 = Ω2 = 40γ; (c) five-level system with Δ1 = − 20γ, Δ2 = 0, Δ3 = 20γ, Ω1 = Ω2 = Ω3 = 40γ; and (d) six-level system with Δ1 = − 20γ, Δ2 = −10γ, Δ3 = 10γ, Δ4 = 20γ, Ω1 = Ω2 = Ω3 = Ω4 = 40γ.
In this scheme, each band for nonreciprocal propagation of light can be well controlled and shifted individually by changing the detuning of the corresponding coupling field, which brings us great convenience for optical signal or information processing. Figure 3 shows the transmissions of the co-propagating and counter-propagating probe fields with different detunings of the coupling fields in the five-level atomic system. It can be seen in Figs. 3(a)–3(c), with the fixed detunings and , the central frequency of the middle nonreciprocal band is shifted independently by tuning . Clearly, the left and right nonreciprocal bands can also be controlled by changing and , respectively. Such frequency-tunable multi-band nonreciprocity may be very helpful in the processing of optical multi-band signals.
Figure 3.Tunable nonreciprocal frequency bands in the five-level atomic system with Δ2 = 0, Ω1 = Ω2 = Ω3 = 40γ, Δ1 = −30γ, Δ3 = 30γ and (a) Δ2 = 20γ; (b) Δ2 = 0γ; (c) Δ2 = −20γ. The other parameters are the same as in Fig.
Bandwidth of optical nonreciprocal devices plays an important role in applications[
Figure 4.Variation of transmission of probe fields with (a), (b) Δp and Ω0 or (c), (d) Ω2, where (a), (c) are the results for the counter-propagating probe field and (b), (d) for the co-propagating probe field. In the calculation, Δ1 = −30γ, Δ2 = 0, Δ3 = 30γ, and the other parameters are the same as in Fig.
To further examine transmissivity and contrast for the case of Figs. 3(c) and 3(d), we calculate and plot the transmissivity and corresponding transmission contrast at the central frequencies of the three nonreciprocal bands in Fig. 5. As shown in Fig. 5(a), transmission of the probe field at is enhanced obviously with the increase of , while at the other two nonreciprocal bands the probe fields have little change. This provides us with a way to flexibly control transmission of signals in need in the nonreciprocal windows. It is anticipated that high transmissions of the probe fields at different nonreciprocal bands can be achieved via increasing the corresponding intensities of the coupling fields. Figure 5(b) shows high transmission contrasts at the center of the three nonreciprocal bands, implying excellent isolation performance of them.
Figure 5.Variations of (a) transmissivity T of the counter-propagating probe field and (b) corresponding transmission contrast η with Rabi frequency of the coupling field Ω2 at the center frequencies of the three nonreciprocal bands, corresponding to the cases of Figs.
It is necessary to have further discussion on the experimental feasibility and possible atomic systems. In the calculation, we have assumed for simplicity, where the effect for the Doppler shift can be well canceled for the probe field in the counter-propagating directions. Generally speaking, it is not easy to find proper atomic transitions. However, Zeeman splitting levels in an alkali metal atomic system such as rubidium and cesium can provide a feasible way for realizing this model. For example, we can choose the transition (384.23034 THz) as the probe field coupled levels and make the control fields with different polarizations couple the transitions (386.25231 THz) in Rb-87 atoms [as shown in Fig. 6(a)]. Then, in similar configurations, it can be greatly guaranteed that . Even for , the absorption can still be largely reduced in the counter-propagating direction, and thus nonreciprocity forms due to the partially eliminated Doppler effect and Doppler broadened linewidth of thermal atoms. For example, we can choose the atomic system and the laser coupling scheme, as shown in Fig. 6(b), where the probe laser couples the transition , and the control laser couples the transitions (; ; ). In this case, and are used for calculation. It can be found that, as long as and are not too different, the property of nonreciprocity can be well kept. The only difference is that the transmission of the probe field in the counter-propagating direction may be suppressed slightly, or part of the multi-band signals cannot be well separated (as shown in Fig. 7). Therefore, multi-band nonreciprocity can also be achieved by using similar multi-level transitions in alkali-metal atoms, such as rubidium and cesium. For example, transitions of in rubidium provide the possibility of cascade-like transitions. In addition, small tilt angles between the probe and coupling fields may also be arranged for matching the condition of in experiment.
Figure 6.Possible atomic systems and laser coupling schemes in experiments, where probe and control fields are with (a) adjacent frequencies by using Zeeman splitting levels and (b) different frequencies.
Figure 7.Transmission of the probe field in counter-propagating (blue solid line) and co-propagating (red dashed line) directions by using the scheme in Fig.
4. Conclusions
In conclusion, based on the EIT effect, we have investigated controllable multi-band nonreciprocal propagation of optical signals in the thermal multi-level cascade atomic systems. By use of multiple strong coupling fields, the weak probe field can propagate with several separated high transmission bands in the opposite direction of the coupling fields due to the EIT effect, while the co-propagating probe field can be well absorbed in the same frequency domain. This provides the possibility of generating and flexibly controlling multi-band nonreciprocal propagation of optical signals. Moreover, separation, bandwidth, and center frequencies of these nonreciprocal transmission bands can be well adjusted and controlled by changing the Rabi frequencies and detunings of the coupling lasers. Simultaneously, high transmission contrast can be maintained in these nonreciprocal bands, guaranteeing excellent optical isolation performance. This work may provide references for related optical isolation devices such as an optical diode and circulator. Other probable functions of the separated nonreciprocal bands may be extracting and discriminating optical signals, which may find application in optical information processing and optical networking.
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Shengfa Fan, Yihong Qi, Yueping Niu, Shangqing Gong, "Nonreciprocal transmission of multi-band optical signals in thermal atomic systems," Chin. Opt. Lett. 20, 012701 (2022)
Category: Quantum Optics and Quantum Information
Received: Jun. 14, 2021
Accepted: Sep. 6, 2021
Published Online: Nov. 11, 2021
The Author Email: Yihong Qi (qiyihong@ecust.edu.cn)