Nonreciprocal Amplification with Four-Level Hot Atoms

Optical nonreciprocity is of paramount importance to optical signal processing and one-way optical communication. Here, we theoretically and experimentally demonstrate nonreciprocal amplification based on four-level hot atoms by exploiting atomic Doppler shifts. Our approach is simple and easy to implement. In fair agreement with our theoretical modeling, forward power amplification of 26 dB and backward isolation of 30 dB are observed. Our results will open up a new avenue towards realistic devices based on nonreciprocal amplification.

Figure 1

(a) Schematic of nonreciprocal amplification via atomic Doppler shifts. A control field and a copropagating pump field drive an atomic medium. The forward probe laser goes through the medium with amplification whereas the backward probe laser tuned at the same transition is absorbed by the medium. (b) The level structure of four-level atoms with two lower states $|1⟩$ and $|2⟩$ and two higher states $|3⟩$ and $|4⟩$. The control field drives the transition $|1⟩\leftrightarrow |3⟩$, the pump field drives the transition $|2⟩\leftrightarrow |4⟩$, and the probe field is near resonance with the transition $|2⟩\leftrightarrow |3⟩$. (c) Dressed states with Doppler shifts accounted for, for forward and backward probe fields, respectively. For two near-resonance gain transition channels $|3+⟩\leftrightarrow |2+⟩$ and $|3-⟩\leftrightarrow |2-⟩$, they are almost Doppler-free in the case of forward propagation but still significantly Doppler broadened in the case of backward propagation.

Figure 2

Theoretical nonreciprocal amplification coefficients ${\alpha }_f$ and ${\alpha }_b$ versus the strength of the control and pump fields for forward (a) and backward (b) propagation of the probe field. Parameters: The detunings are ${\mathrm{\Delta }}_p={\mathrm{\Delta }}_c={\mathrm{\Delta }}_d=0$. To better reflect our experimental system and better fit our experimental results, the spontaneous decay rate and dephasing rate of the concerned atomic transitions are modeled by $\{{\mathrm{\Gamma }}_{31},{\mathrm{\Gamma }}_{32},{\mathrm{\Gamma }}_{41},{\mathrm{\Gamma }}_{42},{\mathrm{\Gamma }}_{21}\}=2\pi \times \{4.2+\beta N,4.2+\beta N,5.6+\beta N,2.8+\beta N,0.1+\beta N\}\mathrm{MHz}$, where $N=2\times {10}^{18}/{\mathrm{m}}^3$ and the broadening coefficient is assumed to be $\beta =0.6\times {10}^{-18}{\mathrm{m}}^3$. The transition dipole moment for the probe field is $u_p=1.4\times {10}^{-29}\mathrm{C}\mathrm{m}$. The wave vector of the probe field is given by $k_p=2\pi /{\lambda }_p$, with ${\lambda }_p=795\mathrm{nm}$.

Figure 3

(a) Experimental observation of normalized forward and backward transmission versus the detuning of the probe field, with pump field power $I_d=55.0\mathrm{mW}$, control field power $I_c=16.0\mathrm{mW}$, and temperature $T=80°\mathrm{C}$. (b) The normalized on-resonance transmission of the probe field versus pump field power at temperature $80°\mathrm{C}$, with the control field power fixed at 16.0 mW. (c) The normalized on-resonance transmission versus the control field power at temperature $80°\mathrm{C}$, with the pump field power fixed at 55.0 mW. (d) The normalized on-resonance transmission versus temperature, with pump field power fixed at 55.0 mW and control field power fixed at 12.0 mW. In (b)–(d) the dots are experimental results and the dashed lines represent theoretical fittings. Theoretical results are obtained with transition dipole moment $\{u_p,u_c,u_d\}=\{1.4,1.4,0.5\}\times {10}^{-29}\mathrm{C}\mathrm{m}$ and effective medium length $L_{\mathrm{eff}}=5\mathrm{cm}$, and other parameters chosen the same as those in Fig. 2. The probe field power is kept at $I_p=0.1\mu \mathrm{W}$ for (a)–(d).

Figure 4

Rabi frequencies of three laser fields versus propagation length. The input Rabi frequencies of the probe, control, and pump fields are $2\pi \times 0.5\mathrm{MHz}$, $2\pi \times 60\mathrm{MHz}$, and $2\pi \times 41\mathrm{MHz}$, respectively. Other parameters are the same as in Fig. 2.