Generating microwave photon Fock states in a circuit QED via invariant-based shortcuts to adiabaticity

Abstract

Optimal generation of photon Fock states is of significance to quantum science and technology.Here we develop a theoretical scheme for fast generating microwave photon Fock states in a circuit quantum electrodynamics (QED) via invariant-based shortcuts to adiabaticity. A superconducting transmon qubit is dispersively coupled to a cavity field of transmission line resonator. Two classical drivings are applied to a composite system, consisting of a transmon qubit and cavity field. In the two-photon resonance with a large intermediate-level detuning, a single-photon Fock state can be fast created by inversely engineering Rabi couplings. With the assistance of auxiliary driving, qubit state can be initialized for inducing multi-photon Fock states in the shortcut manner. Due to negligible leakage effects and high robustness, our scheme offers a potential way to rapidly prepare photon Fock states with a superconducting qubit in circuit QED.

Speeding up generation of photon Fock state in a superconducting circuit via counterdiabatic driving*

“…A driving Ṽs = V s cos(ω s t) with microwave frequency ω s is applied to the CPB, giving rise to the coupling between |g and |e of interest. The interaction Hamiltonian between the qubit and microwave field Ṽs is expressed as [43]…”

“…The amplitude peaks of Ωp,s /2π are about 0.25 GHz, which are accessible in superconducting artificial atoms. [43] Meanwhile, the smooth profiles of Ωp,s are beneficial to experimental realization. Note that in the current condition of pulse calibration technology, the modified drivings Ωs ( Ωp ) having a non-zero value at the initial (final) time t = 0 (t f = 40 ns) could be accessible.…”

“…The reduced density matrix ρ (regarding |e0 , |e1 , and |g1 ) can be obtained by tracing over the environmental degrees of freedom. In the Born-Markov approxima-tion, the time evolution of ρ is described by the Lindblad master equation [43] dρ dt…”

“…Assume that the characteristic parameters of the transmon-type CPB satisfy ĒJ /E c = 50, with E c /h = 2π × 321 MHz. [43] We address a dominant leakage from |e to | f , where | f is the second excited state of the transmon system. Here the microwave driving (with a frequency ω s ) is largely detuned to transition frequencies ω f e and ω eg .…”

“…Very recently, a theoretical scheme has been proposed for the generation of microwave photon Fock states in a circuit QED by the method of invariant-based STA, [43] in which Rabi couplings were specially designed via polynomial ansatz for implementing the coherent process. Differently, although the pulse profile of counterdiabatic driving is generally continuous and smoothed, the counterdiabatic driving behaving as an auxiliary term needs to be added to a reference Hamiltonian.…”