Collision-Induced Broadband Optical Nonreciprocity

Chao Liang, Bei Liu, An-Ning Xu, Xin Wen, Cuicui Lu , Keyu Xia , Meng Khoon Tey, Yong-Chun Liu , and Li You State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan 250358, China College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China Frontier Science Center for Quantum Information, Beijing 100084, China

Despite the rapid progress in this area, it remains a major challenge to realize optical nonreciprocity with a high isolation ratio, broad bandwidth, and low insertion loss simultaneously. In previous studies, many approaches make use of optical cavities [39][40][41][42][43][44][45][46][47], which can realize a high isolation ratio due to the cavity-enhanced interaction, but the bandwidth is inherently limited by the cavity linewidth, typically less than 10 MHz. Other schemes achieve a broad isolation bandwidth, but the isolation ratios are relatively low due to relatively weak interactions [48,49].
Here we experimentally realize high-performance magnet-free and cavity-free optical nonreciprocity, which simultaneously possesses an ultrahigh isolation ratio and ultrabroad bandwidth, as well as low insertion loss. By taking advantage of the random motion and collision of thermal atoms, we realize direction-dependent population trapping of the atoms, leading to the nonreciprocal behavior for the probe laser passing through the atoms. By combining multiple resonance enhancements, the isolation ratio reaches as high as 40 dB, the bandwidth for isolation ratios exceeding 20 dB is over 1.2 GHz, and the insertion loss is less than 1 dB. These results represent a bandwidth that is over 2 orders of magnitude broader than typical resonance-enhanced optical isolators. In addition, the dynamic range of isolated light power spans more than 1 order of magnitude. Thus, this Letter opens up realistic opportunities for practical applications in optical signal processing.
The schematic diagram for our experimental setup is shown in Figs. 1(a) and 1(c). A cubic glass cell (side length 1 cm) is filled with gaseous rubidium-87 ( 87 Rb) atoms and buffer gas (helium-4 and nitrogen). The pressure of the buffer gas is 30 Torr, and the temperature of the cell is stabilized at 75°C unless otherwise specified. Three laser beams are used: switching and coupling lasers for controlling the atoms and a probe laser for examining optical nonreciprocity. The propagation directions of the switching and coupling lasers are the same, while the prorogation direction of the probe laser can be the same as (copropagating case) or opposite to (counterpropagating case) the switch and coupling lasers. The polarization of the probe laser is perpendicular to the polarization of the switching and coupling lasers so that the transmitted signal of the probe laser can be separately measured.
The energy level diagrams of the atoms are shown in Figs. 1(b) and 1(d) for the copropagating and counterpropagating cases, respectively. The switching, coupling, and probe lasers drive the transitions j5 2 S 1=2 ;F¼1i⇔ j5 2 P 1=2 ;F¼1iðj1i⇔j2iÞ, j5 2 S 1=2 ;F ¼ 2i ⇔ j5 2 P 1=2 ;F ¼ 1i ðj3i ⇔ j2iÞ, and j5 2 S 1=2 ;F¼2i⇔j5 2 P 1=2 ;F¼2iðj3i⇔j4iÞ, respectively. Their Rabi frequencies and wave numbers are correspondingly denoted by (Ω s , Ω c , Ω p ) and (k s , k c , k p ). The detunings of the three lasers from their respectively coupled transitions are denoted by (Δ s , Δ c , Δ p ). For atoms moving with a velocity v, the detunings change into (Δ s þ k s v, Δ c þ k c v, Δ p þ k p v) for the copropagating case and (Δ s þ k s v, Δ c þ k c v, Δ p − k p v) for the counterpropagating case due to Doppler shift. In the rotating reference frame and undepleted control field approximation, the Hamiltonian for this group of atoms reads 4Þ are the atomic transition operators. Here the difference between H co and H cou for copropagating and counterpropagating is the term AEk p vσ 44 , with þ for the former and − for the latter. Since the frequency differences among the three lasers are quite small compared to their absolute frequencies, k s , k c , and k p are essentially equal and can be uniformly denoted by k. By solving the master equation _ ρ ¼ −i½H co=cou ; ρ þ L½ρ with L½ρ being the Lindblad operator describing the decay and dephasing of the atoms, we can calculate the stationary density matrix elements and obtain the transmission for the probe laser [50]. To understand the emergence of nonreciprocity, we focus on the atomic velocity distribution in level j3ĩ ρ ðco=couÞ 33 is the most probable speed of atoms, k B is the Boltzmann constant, T is the temperature of the atomic gas, and m is the mass of the atom. In the absence of the switching and coupling lasers, the system is reciprocal because the atomic velocity distributions are symmetric for forward and backward directions. The presence of switching and coupling lasers breaks such a symmetry. Then,ρ co 33 ðvÞ andρ cou 33 ðvÞ become quite different, leading to optical nonreciprocity for the probe laser (see the Supplemental Material [50] for more details).
The experimental results for the typical transmission spectra of the probe laser are plotted in Fig. 2(a). It shows that the probe field exhibits a high transmittance in the counterpropagating case (T cou , red dots), while it is strongly absorbed in the copropagating case (T co , blue dots). These experimental results are in good agreement with the theoretical curves plotted in Fig. 2(b) (details in the Supplemental Material [50]). To quantitatively describe the optical nonreciprocity, we introduce the isolation ratio 10 log 10 ðT cou =T co Þ and contrast ratio ðT cou − T co Þ=ðT cou þ T co Þ. As shown in Fig. 2(c), the maximum isolation ratio reaches nearly 40 dB (green dots), corresponding to a contrast ratio of 0.9999 (pink dots).
As revealed in Fig. 2, the isolation works in a remarkably broad frequency range. For convenience, we define the 20 dB isolation bandwidth, which corresponds to the frequency range where the isolation ratio is larger than 20 dB (with a contrast ratio larger than 0.99). Our typical , which is more than 200 times broader than the atomic natural linewidth. This ultrabroadband nonreciprocity originates from two aspects: atomic collision and multiple resonance enhancements. First, unlike typical experiments where atomic collisions often bring in detrimental effects, here we fill the vapor cell with buffer gas to enhance the collision between the rubidium atoms and the buffer gas atoms. This collision destroys the atomic coherence, which makes the atoms relax more rapidly. When the probe laser interacts with the atoms, the absorption linewidth becomes broader. This also leads to the broadening of the nonreciprocal bandwidth as long as this broadening is still comparable to the Doppler linewidth. In our experiments with 30 Torr buffer gas and a temperature of 75°C, the Doppler broadening is about 540 MHz, while the collision broadening is around 570 MHz [51]. In this case, the bandwidth can be strongly broadened while the high isolation ratio is preserved. Further increasing the buffer gas density and the temperature leads to an even broader isolation bandwidth (see Supplemental Material [50] for more results). Second, we have made use of multiple resonance enhancements to further increase the isolation bandwidth. The energy levels j2i and j4i correspond to the hyperfine splitting energy levels j5 2 P 1=2 ; F ¼ 1i and j5 2 P 1=2 ; F ¼ 2i of 87 Rb atoms, which are separated by 814 MHz. Due to the collision induced broadening, the nonreciprocal bandwidth becomes comparable to this energy level separation. Therefore, the nonreciprocal windows for these two energy levels overlap and merge, leading to the formation of a broadened nonreciprocal window. As shown in Figs. 2(a)-(c), the separation between the two dips (peaks) is about 0.8 GHz, which exactly matches the hyperfine splitting above, showing that the two dips (peaks) correspond to two resonance transitions, j3i ⇔ j4i and j3i ⇔ j2i.
Moreover, as shown in Fig. 2(a), the typical transmittance observed within the 20 dB isolation bandwidth exceeds 0.8, corresponding to an insertion loss less than 1 dB [50]. These properties of a high isolation ratio, ultrabroad bandwidth, and low insertion loss can also persist for a significant range of probe laser power-from 10 to 150 μW-as plotted in Fig. 2(d) (see Supplemental Material [50] for more results). Note that our scheme is void of the dynamic reciprocity problem [10,52] because the nonreciprocity realized here originates from the atomic motion, which breaks the time reversal symmetry, instead of directly from the nonlinearity of the atoms. This feature has great potential for practical applications.
In Fig. 3, we display the measured probe laser transmission spectra for copropagating and counterpropagating settings at different control laser powers. As we fix the switching laser power at P s ¼ 2.2 mW and increase the coupling laser power P c , the copropagating transmission keeps near 0 and changes only slightly [ Fig. 3(a)], while the counterpropagating transmission increases strongly from 0 to 0.8 [ Fig. 3(b)]. This finding reveals that the coupling laser has little effect on the transmission of the probe laser for the copropagating case but strongly influences the counterpropagating case. The increase of the counterpropagating transmission originates from the fact that a stronger coupling laser drives more atoms from state j3i to state j1i and thus the absorption for the probe laser becomes weaker. On the other hand, as we fix the coupling laser power at P c ¼ 2.4 mW and increase the switching laser power P s , the copropagating transmission decreases strongly from approximately 0.8 to 0 [Fig. 3(c)], while the counterpropagating transmission keeps near 0.8 and changes only slightly [ Fig. 3(d)]. This finding shows that the switching laser has a strong (small) effect on the copropagating (counterpropagating) case, which is just opposite to the coupling laser's effect. The reason is that the switching laser drives atoms from state j1i to state j3i, which plays an opposite role compared with the coupling laser. Note that the control laser power required to obtain high-performance nonreciprocity is less than 3 mW, which is practical for applications. Meanwhile, the nonreciprocity does not strictly rely on the detuning of the switching and coupling lasers, which can tolerate errors in the GHz range [Figs. 3(e) and 3(f)], revealing that our scheme is robust to system parameter changes. Furthermore, our system is also capable of realizing bidirectional nonreciprocity. As shown in Figs. 4(a) and 4(b), with other experimental conditions fixed, as we sweep the probe laser detuning from −5 to 10 GHz, two nonreciprocal windows appear. In addition to the first nonreciprocal window near Δ p ¼ 0, which has been discussed previously, a second nonreciprocal window appears near Δ p =2π ¼ 6.8 GHz. The response of the copropagating and counterpropagating probe fields for the second nonreciprocal window becomes opposite to that of the first nonreciprocal window, i.e., the copropagating probe laser can pass through while the counterpropagating probe laser is absorbed. This bidirectional nonreciprocity originates from the different coupling routes for the probe laser with different laser frequencies. As sketched in Figs. 4(c) and 4(d), the first nonreciprocity window is related to the transition j3i ⇔ j2i and j3i ⇔ j4i, while the second nonreciprocity window is associated with the transition j1i ⇔ j2i and j1i ⇔ j4i. The hyperfine splitting of the two energy levels, j5 2 S 1=2 ; F ¼ 1i (j1i) and j5 2 P 1=2 ; F ¼ 2i (j3i) of 87 Rb atoms, is 6.8 GHz, which exactly matches the distance of the two nonreciprocity windows. Since the roles of switching and coupling lasers just reverse for these two cases, it is clear that the two nonreciprocity windows just exhibit opposite properties. As shown in Fig. 4(b), we can realize high-performance nonreciprocity for both windows, with the isolation ratio greater than 20 dB, and the isolation bandwidth exceeding 1 GHz.
It is worth noting that our approach is essentially different from the typical nonreciprocity electromagnetically induced transparency (EIT) effect [35,36], The EIT effect takes advantage of the coherence of atoms, but our mechanism makes use of strong atomic collisions, which strongly destroy the coherence. The typical nonreciprocal EIT bandwidth is on the order of 10 MHz, which is limited by the intrinsic atomic resonance linewidth, while in our experiments a nonreciprocal bandwidth of over 1.2 GHz has been observed. Due to the distinct mechanism, the transmission line shapes in our scheme are also different from the typical EIT line shape. In addition, bidirectional nonreciprocity can be realized in our experiments by simply tuning the probe laser frequency, which is not realizable in the EIT scheme.
In summary, we have experimentally demonstrated simultaneously high isolation ratio, ultrabroad bandwidth, and low insertion loss for optical nonreciprocity in a thermal atomic vapor cell, with an isolation ratio close to 40 dB, a 20 dB isolation bandwidth exceeding 1.2 GHz, and an insertion loss less than 1 dB. Remarkably, the The corresponding isolation ratio of (a). The shaded regions denote the two nonreciprocal windows with isolation ratios greater than 20 dB. The switching laser power is P s ¼ 2.2 mW, the coupling laser power is P c ¼ 2 mW, and the detunings are 0. (c),(d) Energy level diagrams for the first (c) and second (d) nonreciprocal windows.
operating bandwidth represents an improvement of over 2 orders of magnitude compared to the typical resonanceenhanced optical isolators. This result originates mainly from the atomic collision effect, which is usually regarded as an undesirable process for most experiments. Aided by multiple resonance enhancements, the bandwidth is further broadened, while the high isolation ratio is still maintained. Furthermore, our scheme is promising for miniaturization and integration using atomic cladding waveguides on a chip [53][54][55][56][57][58] or hollow-core photonic crystal fibers [59,60]. Therefore, our study paves the way for realizing highperformance nonreciprocal devices with potential applications in integrated optics and quantum networks, and it may also inspire the exploration of the potential influence of the anomalous Doppler effect [61,62] on the nonreciprocal phenomenon.