Single microwave photon switch controlled by an external electrostatic field

We design a single microwave photon switch through a one-dimensional waveguide coupled with a side Jaynes-Cummings system, namely, a single-mode cavity with an embedded Rydberg atom ${}^{87}\mathrm{Rb}$. Since the energy spectra of the ${}^{87}\mathrm{Rb}$ atom depend on the electrostatic field, the ${}^{87}\mathrm{Rb}$ atom can couple with the cavity in tune and out of tune, corresponding to the switch on and off states, respectively. The influences of the single photon pulse width, cavity dissipation, and Rabi coupling on the on/off ratio are studied in detail by a non-Hermitian Hamiltonian. We find that the on/off ratio can be larger than 100 in a wide parameter space and the decay time and rise time are both about 0.75 ns. Within the master equation of the density matrix we also demonstrate that the on/off ratio can be reduced by the quantum noise but is still large enough for application. The transition energy of the two-level Rydberg atom ${}^{87}\mathrm{Rb}$ gives the switch operating frequency which is in the range of microwave regime. Accordingly, the switch is viable in practice and has potential in quantum informatics.

Figure 1

(a) Schematic diagram of a one-dimensional waveguide side coupled with a cavity with eigenfrequency of ${\omega }_c$. The yellow wave curve stands for a single photon pulse in the waveguide whose coupling with the cavity is denoted by the pink arrow. In the cavity a ${}^{87}\mathrm{Rb}$ atom is embedded and the energies of its Rydberg states can be tuned by an external voltage difference of $U$. (b) Concerned energy spectra for ${}^{87}\mathrm{Rb}$ in the electrostatic field (due to the direct current Stark shifts of Rydberg states), refer to Ref. [44] for details. In calculation we focus on the transition frequency range of $[{\omega }_1,{\omega }_2]=[2.7{\omega }_0,0.7{\omega }_0]$ with ${\omega }_0=2\pi \times {10}^{10}$ Hz, where ${\omega }_1$ and ${\omega }_2$ correspond to an electrostatic field of 530 and 545.9 V/cm, respectively.

Figure 2

(a–c) Transmission spectra of the single photon pulse with $k_w=0.01k_0$ and $0.1k_0$ for the tuning and detuning couplings between the cavity and atom; (d–f) Variation of the transmissivity (solid black and dashed red curves, left axes) and on/off ratio (dotted blue curves, right axes) with $k_w$ when ${\varepsilon }_i=2.7{\omega }_0$. Parameters: $g=0.09{\omega }_0$ and ${\gamma }_c={\gamma }_a=0$.

Figure 3

Variation of the transmissivity (solid black and dashed red curves, left axes) and on/off ratio (dotted blue curves, right axes) with $k_w$ under several different losses of the cavity and atom. Parameters: $g=0.09{\omega }_0,V_0/{\lambda }_0^{0.5}=0.1{\omega }_0$, and ${\varepsilon }_i=2.7{\omega }_0$.

Figure 4

Variation of the transmissivity (solid black and dashed red curves, left longitudinal axes) and on/off ratio (dotted blue curves, right axes) with $g$ under several losses of the cavity. Parameters: $V_0/{\lambda }_0^{0.5}=0.1{\omega }_0,{\varepsilon }_i=2.7{\omega }_0,k_w=0.02k_0$, and ${\gamma }_a=0$.

Figure 5

(a) Contour map of the waveguide photon probability density (normalized to its maximum value denoted by “Max”) as functions of $x$ and $t$ for the switch first turning on and then off and (b) the probability distributions when $t=20{\tau }_0$ (dashed black), $200{\tau }_0$ (dotted dark yellow), and $300{\tau }_0$ (solid red), corresponding to those in (a). The denotations for (c) and (d) are the same as those for (a) and (b), except the switch first turning off and then on. Parameters: $V_0/{\lambda }_0^{0.5}=0.1{\omega }_0,g=0.09{\omega }_0,k_w=0.01k_0,{\gamma }_c=0.005{\omega }_0$, and ${\gamma }_a=0$.

Figure 6

(a) Contour map of the waveguide photon probability density (normalized to its maximum value) as functions of $x$ and $t$ for the switch on state and (b) corresponding time evolution of $n_r$ and $n_l$. (c) and (d) are the same as (a) and (b), respectively, except for the switch off state. Parameters: $V_0/{\lambda }_0^{0.5}=0.1{\omega }_0,{\varepsilon }_i=2.7{\omega }_0,g=0.09{\omega }_0,k_w=0.01k_0,{\gamma }_c=0.005{\omega }_0$, and ${\gamma }_a=0$.