Experimental demonstration of Cavity-Free Optical Isolators and Optical Circulators

Cavity free optical non reciprocity components, which have an inherent strong asymmetric interaction between their co and counter propagation direction, are key to produce such as optical isolators and circulators. According to the proposal presented in [Phys Rev Lett. 121, 203602 (2018)], we experimentally build a device that uses cross Kerr nonlinearity to achieve cavity free optical isolator and circulator. Its nonreciprocity behavior arises from the thermal motion of N type configuration atoms which induces a strong chiral cross Kerr nonlinear response for the weak probe beam. We obtain a two-port optical isolator up to 20 dB of isolation ratio in a specially designed Sagnac interferometer. The distinct propagation directions of the weak probe field determine its cross-phase shift and transmission, by which we demonstrate the accessibility of a four port optical circulator.

Introduction.-Non-reciprocityoptical devices that break the time-reversal symmetry are very difficult to achieve without magnetic fields, such as optical isolators and circulators [1].To break reciprocity, the traditional method is to guide light through a medium with a powerful magneto-optical Faraday effect [2,3].However, systems with this nature often have serious conflicts with miniaturization and integration due to the surrounding environmental interference from their strong magnetic fields.The requirements of a non-magnetic isolator have generated tremendous impetus, and then a series of works in various physical principles are reported to avoid using magneto-optical components.For example, the different types of optical non-reciprocity devices have been realized by using spatiotemporal modulation of non-linear material [4][5][6][7][8][9][10], inducing the Berry phase [6,[11][12][13], and using optomechanical systems [13][14][15][16][17].
To realize optical isolators with the Kerr and Kerrlike nonlinearity is attracting many researchers [18][19][20][21][22][23][24].However, the optical isolators with the Kerr and Kerrlike nonlinearity has a poor isolation effect under the weak signals due to the limitation of dynamic nonreciprocity [25,26].Some nonlinear optical isolators with chiral gains are reported to overcome this difficulty in [27,28].Besides, the nonlinear optical isolation schemes require high-quality cavity to achieve enough interaction strength, such as optical resonators [20,27,[29][30][31][32].Although the fundamental aspects of optical nonreciprocity have been studied before, it is challenging to achieve an optical non-reciprocity with high isolation, low loss, and weak light intensity simultaneously.Therefore, a passive nonlinear isolator without dynamic reciprocity would be of interest and is proposed by [31].
Here, we demonstrate a cross-Kerr nonlinearity based on an N -type atomic configuration in a thermal vapor cell to achieve a cavity-free optical isolator and circulator.The cross-Kerr nonlinearity affects the transmission and susceptibility of the input weak probe field dramatically, this process depends on the coupling and switch fields' forward-and backward-propagating directions with respect to the probe field.Hence, we achieve a cross-Kerr optical isolator with up to 20 dB of isolation ratio.In addition, we demonstrate a four-port optical circulator via a specially designed Sagnac interferometer.The reported cross-Kerr optical isolator and optical circulator could work under high isolation, low loss, and weak field, which holds potential applications for quantum communication [33], quantum simulation [34], quantum information processing [35].
System configurations.-Weuse a N -type atomic configuration in thermal rubidium ( 85 Rb) atoms to demonstrate the cross-Kerr nonlinearity [36][37][38].As shown in Fig. 1 (a), the coupling and switch lasers with vertical polarization couple the atomic transitions The probe laser with horizontal polarization couples the transition The Rabi frequencies and detunings of the probe, coupling, and switch fields are, respectively, denoted by Ω p (∆ p ), Ω c (∆ c ), and Ω s (∆ s ).The spontaneous decay rates of the state |2 (|4 ) to the states |1 and |3 are Γ 21 (Γ 41 ) and Γ 23 (Γ 43 ), respectively.The dephasing rate between the two ground states |1 and |3 is Γ 31 .In the rotating-wave approximation, the Hamiltonian under interaction picture describing the field-atom interaction takes the form, where σ mn = |m n| (m, n = 1, 2, 3, 4) are the atomic transition operators.Due to atomic thermal motion, the frequencies of the propagating fields seen by the atoms are shifted, which is referred to as the directional Doppler effect.The detunings of the probe, coupling, and switch field are then modified as ∆ p ± k p ν, ∆ c ± k c ν, and ∆ s ± k s ν, with k p , k c , and k s being the corresponding wave vectors, and the signs '±' depending on the propagation direction.When the probe beams co-propagates with the coupling and the switch field, the Doppler shifts take the same sign, and their effects are generally cancelled.However, when the probe beam counter-propagates with the coupling and the switch field, the Doppler shifts have opposite signs, and thusthe Doppler broadening cannot be ignored.For both the co-and counter-propagation cases, we solve the steady-state solution of the master equation ρ by taking all the decay channels into consideration and obtain the total cross-Kerr nonlinear susceptibility averaged over the velocity distribution as where N 0 is the atomic density, µ 23 is the transition dipole moment between states |2 and |3 , k B is the Boltzmann constant, T is the temperature of the gas in the cell, and M is the atomic mass.χ + 23 (χ − 23 ) represents the probe field co-propagating (counterpropagation) with the coupling and the switch field.The transmission for the probe field is further given by the imaginary part of optical susceptibility Im[χ ±  23 ], which strongly depends on the propagation direction of the probe field regarding the coupling and the switch field, leading to the chiral cross-Kerr nonlinearity.This effect allows us to implement optical isolators and circulators by handling the probe field with fixedly directional coupling and switch fields. .As schematically illustrated in Fig. 1 (b), the specially designed Sagnac interferometer consists of BS1 and three Mirrors M2-M4, which has two different optical paths L1 and L2.This interferometer has four ports consisting of two input ports (port 1 and port 3) and two output ports (port 2 and port 4).We insert PBS1 and PBS2 into the interferometer and add a Rb cell in the optical path L1.To implement isolators and circulators, the most important part is a subsystem including five elements (BS2, M6, PBS1-2, and Rb cell), which can control the transmission and the phase shift of the input probe beam.In this subsystem, the BS2 mixes the coupling and the switch beam into two collinear beams along with the optical directions of C1 and C2 simultaneously.The probe beam splits into two beams along L1 and L2 by the BS1 (beam splitter).Due to the chiral cross-Kerr nonlinearity, the probe beam accumulates different phases shifts while it propagates along the path L1 and the path L2, based on which, we can implement a two-port optical isolator by closing the path L2, or implement an optical circulator with both the L1 and L2 paths being opened.
Isolator.-Weinput the weak probe field with the intensity I p = 7.5µW to measure the co-or counter-propagation transmission.The co-and counterpropagation transmission are given in Fig. 1 (c) and Fig. 1 (d).By changing the switch power I s from 0 mW to 25 mW, we obtain a series of transmission spectra of the co-and counter-propagating probe field in Fig. 2 (a) and Fig. 2 (b).The on-resonance transmission of the probe beam increases in the co-propagation case but remains small for the counter-propagation case.When the combined coupling and switch beams C1 co-propagate with the probe beam, the Doppler shift seen by the atoms have the same sign, and their Doppler effect in the Ntype configuration can be eliminated, thus we can observe a strong response of the probe field to the cross-Kerr nonlinearity.In contrast, the Doppler effect under the counter-propagation case strongly diminishes the cross-Kerr nonlinearity, so we observe that the probe transmission is almost vanishing.The chirality arisen from the asymmetric cross-Kerr nonlinearity directly leads to the direction-dependent response of the probe beam, thus resulting in the non-reciprocal feature of the probe field.
We characterize the property of the isolator by measuring the resonant probe transmission with ∆ p = 0 and by the logarithmic ratio of the co-propagation transmission T co to the counter-propagation transmission T cou , namely 10Log 10 (T co /T cou ) (referred to as the isolation ratio), as shown in Fig. 2(c).There is a significant difference between the on-resonance transmission spectrum of the co-propagation (blue dots) and counter-propagation (red dots).In the co-propagation case, we observe that the increasing of the switch field power I s can significantly enhance the cross-Kerr nonlinear response of the probe field.While the Doppler shift breaks the chiral cross-Kerr nonlinearity in the counter-propagation case, we obtain a series of weak on-resonance transmission signals.Moreover, the isolation ratio increases against I s as predicted by the theory in the article [31].As the switch power increases, the isolation ratio increases to be 20 dB.Even though we scan the switch field power I s only from 0 mW to 25 mW because of the limitation of the laser power in our experiment, we nevertheless find that when the switch field power is tuned exceeding 21 mW, the transmission and the isolation ratio will be suppressed.This is because the atoms would be depleted when using a large power of the switch field to pump.Moreover, we further examine the co-propagation transmission versus the detuning ∆ s of the switch field, with the fixed switch field power I s = 21mW, as shown in Fig. 2(d).For a resonant pumping, i.e. ∆ s =0 MHz, the switch laser will suppress the cross-Kerr nonlinearity, while the off-resonant pumping of the switch field will induce the strong cross-Kerr nonlinear response.In addition, we observe that increasing the power of the switch field produces a magnifying effect on the co-propagation transmission of the probe field.Remarkably, all the experimental data (dots) fit well with our theoretical prediction (dash-line), thus fully confirming our physical insights and theoretical analysis above.
Circulator.-We unblock the path L2 and enable the two non-coincident paths of the Sagnac interferometer to work simultaneously, which constructs a four-port optical circulator as proposed in [31].We inject the probe beam into this circulator by port 1, and control the propagation direction of the switch and the coupling beams with C1, C2.While the probe field co-propagates with the other two laser beams, the strong cross-Kerr nonlinearity can not only modify the transmission rate T co , but also introduce a large phase shift φ L1 co to the probe field in contrast to that of the counter-propagating case.As a result, the difference in phase shift for the two non-coincident paths ∆Φ = φ L1 co −φ L2 leads to the interference effect of the two counter-propagating probe fields at the port 2, which can be measured by the phase-dependent intensity fringes.We thus use port 2 to output the interference phenomena by sweeping the probe frequency and record the corresponding phase shift difference ∆Φ, see Fig. 3.As the detuning of the probe beam changes, we observe three different patterns of the phase shift difference ∆Φ by tuning the phase shift offset between the optical paths L1 and L2.For the case at the middle panel of the Fig. 3, it allows us to realize the photon circulation along the path described by the port sequence: 1 → 2 → 3 → 4 → 1.In contrast, while the probe field counter-propagates with the other two laser beams, the transmission T cou and phase shift φ L1 cou are extermely weak, and we cannot observe any circulation under the counter-propagation case.Therefore, we successfully construct a device for implementing a non-reciprocal four-port optical circulator.
Conclusion.-In summary, we have demonstrated an experiment to realize cavity-free optical isolators and circulators by a chiral Cross-Kerr nonlinearity of N -type Rb atoms embedded in the two-path Sagnac interferometer at room temperature.Simultaneously, our isolator can reach a high isolation ratio of 20 dB.Based on the experimental conclusions, we successfully prove that the specific designed experimental device can provide a new version for the optical circulator.Therefore, our design allows us to make optical isolators and circulators for high isolation, low loss, and a weak probe field at room temperature.
Note.When we prepared our manuscript, we found a relative work on nonreciprocal amplification with fourlevel atomic system by Lin et al. [28].

Figure 1 .
Figure 1.(a) Energy diagram of optical isolation and circulation, corresponding to the N -type four states in 85 Rb atoms (D line) of 5S 1/2 (F = 2) (|1 ), 5P 1/2 (F = 3) (|2 ), 5S 1/2 (F = 3) (|3 ), and 5P 3/2 (F = 3) (|4 ), respectively.(b) Schematic overview of the experimental setup, including a sagnac interferometer system.The blue lines represent the probe beam path, red and green lines represent the switch and the coupling laser beams, respectively.M: optical mirrors; BS: beam splitters (50/50); PBS: polarizing beam splitters; HWP: half-wave plates; L1 and L2 are two different paths of the sagnac interferometer, in which a Rb cell located in L1; C1 and C2 are the combined laser beams of switch field and coupling field.(c) The co-propagation transmission versus the detuning of the probe field, the red curve and black curve recorded as the switch power Is=21 mW and Is=0 mW respectively.(d) The counter-propagating (blue curve) transmission versus the detuning of the probe field, with the switch power Is=21 mW.In (c)-(d) the probe field set as Ip = 7.5µW and the coupling field set as Ic = 12mW.

Figure 2 .
Figure 2. Experimental observation of non-reciprocal transmission.(a)-(b) The co-and counter-propagation transmission spectra of the probe beam by increasing switch field power Is, with the probe field power Ip = 7.5µW, the coupling field power Ic = 12mW, and temperature T = 38 • C. (c) The on-resonance transmission of the isolator for the copropagating (blue dots) and counter-propagating (red sots), and the isolation ratio of the isolator (green dots).(d) The onresonance transmission spectra of the probe field versus the detuning of the switch field (violet dots).In (c)-(d) the dots are experimental results and the dashed lines are theoretical fittings.

Figure 3 .
Figure 3. Circulator performance.The three different phase shift versus the probe field detuning ∆p with fixed switch field Is = 12mW , coupling field Ic = 12mW and probe field Ip = 7.5µW.