Nonreciprocal Phonon Blockade in a Spinning Acoustic Ring Cavity Coupled to a Two-Level System

Quantum nonreciprocal devices have received extensive attention in recent years because they can be used to realize unidirectional quantum routing and noise isolation. In this work, we show that the shift of resonance frequencies of propagating phonons induced by spin-orbit interactions of phonons in a rotating acoustic ring cavity can be used to realize nonreciprocal phonon blockade. When driving the cavity from different directions, nonreciprocal single-, two-phonon blockade, and phonon-induced tunneling can take place by varying the parameters of the system to an appropriate value. To realize phonon blockade, a two-level system is employed to induce self-interactions of phonons in the cavity. We also show the possibility of this proposal for designing nonreciprocal phonon routing. This work provides a way to achieve acoustic nonreciprocal devices, such as directional acoustic switches and quantum noise isolation, which may help acoustic information network processing.

Figure 1

Schematic of the composite spin-phononic system. The ring cavity is coupled with the phononic waveguide to the input and output of the driving field, and at the same time coupled to a two-level system to realize phonon blockade. In addition, we add a rotator to the cavity to make the cavity rotate counterclockwise at an angular frequency $\mathrm{\Omega }$. The phonons, which input from the left or right side of the waveguide, rotate counterclockwise or clockwise in the cavity corresponding to (a) or (b), respectively.

Figure 2

$g^{(2)}(0)$ as a function of the nonlinear strength $U$ and the detuning ${\mathrm{\Delta }}_L$, here ${\mathrm{\Delta }}_F=0$. (a),(b),(c),(d) corresponds to the situation when $\xi =0.33\gamma$, $\xi =1\gamma$, $\xi =3\gamma$, and $\xi =5\gamma$, respectively.

Figure 3

(a) Under the weak-driving-strength region $\xi =0.33\gamma$, the correlation function versus the detuning ${\mathrm{\Delta }}_L$ at $U=20\gamma$. (b),(c) show the comparison for 1PB between the correlation function and the standard value in Eq. (18). (d),(e) show the deviation between the phonon population and the Poisson distribution for 1PB and PIT, respectively at ${\mathrm{\Delta }}_L=0$ and ${\mathrm{\Delta }}_L=20\gamma$.

Figure 4

(a) Under the strong-driving region $\xi =3\gamma$, the correlation function versus the detuning ${\mathrm{\Delta }}_L$ at $U=20\gamma$. (b),(c) show the comparison for 2PB between the correlation function and the standard value in Eq. (19). (d),(e) show the deviation between the phonon population and the Poisson distribution for 2PB and PIT, respectively at ${\mathrm{\Delta }}_L=20\gamma$ and ${\mathrm{\Delta }}_L=40\gamma$.

Figure 5

The correlation function $g^{(2)}(0)$ versus the detuning ${\mathrm{\Delta }}_L$ under weak driving $\xi =0.33\gamma$ and nonlinear constant $U=20\gamma$. (a) and (b) is corresponding to the results of driving the cavity from the right side and the left side of the waveguide, respectively.

Figure 6

(a) The correlation function $g^{(2)}(0)$ versus the detuning ${\mathrm{\Delta }}_L$ with $\xi =0.33\gamma$, ${\mathrm{\Delta }}_F=10\gamma$, and $U=20\gamma$. The chain (solid) line is the numerical solution result of driving the system from the left (right) side, and the triangle (square) scatter is the analytical solution result of driving the system from the left (right) side. (b) The energy levels of driving the system from the left side and driving the system from the right side become nonequidistant at ${\mathrm{\Delta }}_L=10\gamma$.

Figure 7

The correlation function versus the detuning ${\mathrm{\Delta }}_L$ with $\xi =3\gamma$, ${\mathrm{\Delta }}_F=10\gamma$, and $U=20\gamma$.

Figure 8

(a) Energy levels of driving the system from the left and driving the system from the right side become nonequidistant for ${\mathrm{\Delta }}_L=10\gamma$. (b),(c) show the comparison for 2PB between the correlation function and the standard value in Eq. (19), (d),(e) show the deviation of the phonon population and the Poisson distribution for 1PB and 2PB, respectively.

Figure 9

(a) Under the strong-driving-strength region $\xi =3\gamma$, the energy levels of driving the system from the left and driving the system from the right side become nonequidistant for ${\mathrm{\Delta }}_L=30\gamma$. (b),(c) show the comparison for 2PB between the correlation function and the standard value in Eq. (19), (d),(e) show the deviation of the phonon population and the Poisson distribution for 2PB and PIT, respectively.

Figure 10

(a) Phonons input from both sides of the waveguide can be transmitted to the other end. (b) The phonons input from both sides of the waveguide can only be transmitted to the other end in the form of a single phonon. (c) Phonons input from both sides of the waveguide, one side can be transmitted to the other end, and the other side can only be transmitted to the other end in the form of a single phonon. (d) For phonons input from both sides of the waveguide, one side can only be transmitted to the other end in the form of a single phonon, and the other side can only be transmitted to the other end in the form of two phonons.

Figure 11

Possible setup for experimental implementation. Surface acoustic waves can be generated by an interdigital transducer (IDT), which travel via a waveguide and output from the IDT at the other end. Epitaxially grown layers of piezoelectric material make up the waveguide and ring cavity. Qubits fabricated on or inside the substrates, such as superconducting qubits, or spin qubits, can be used to realize the qubit-phonon coupling.