We discuss level splitting and sideband transitions induced by a modulated coupling between a superconducting quantum circuit and a nanomechanical resonator. First, we show how to achievean unconventional time-dependent longitudinal coupling between a flux (transmon) qubit and the resonator. Considering a sinusoidal modulation of the coupling strength, we find that a first-order sideband transition can be split into two. Moreover, under the driving of a red-detuned field, we discuss the optical response of the qubit for a resonant probe field. We show that level splitting induced by modulating this longitudinal coupling can enable two-color electromagnetically induced transparency (EIT), in addition to single-color EIT. In contrast to standard predictions of two-color EIT in atomic systems, we apply here only a single drive (control) field. The monochromatic modulation of the coupling strength is equivalent to employing two eigenfrequency-tunable mechanical resonators. Both drive-probe detuning for single-color EIT and the distance between transparent windows for two-color EIT, can be adjusted by tuning the modulation frequency of the coupling.

We describe a hybrid quantum system composed of a micrometer-size carbon nanotube (CNT) longitudinally coupled to a flux qubit. We demonstrate the usefulness of this device for generatinghigh-fidelity nonclassical states of the CNT via dissipative quantum engineering. Sideband cooling of the CNT to its ground state and generating a squeezed ground state, as a mechanical analogue of the optical squeezed vacuum, are two additional examples of the dissipative quantum engineering studied here. Moreover, we show how to generate a long-lived macroscopically-distinct superposition (i.e., a Schr\“odinger cat-like) state. This cat state can be trapped via dark-state methods assuming that the CNT dissipation is negligible compared to the qubit dissipation, and can be verified by detecting the optical response of control fields.

Single-photon devices at microwave frequencies are important for applications in quantum information processing and communication in the microwave regime. In this work, we describea proposal of a multi-output single-photon device. We consider two superconducting resonators coupled to a gap-tunable qubit via both its longitudinal and transverse degrees of freedom. Thus, this qubit-resonator coupling differs from the coupling in standard circuit quantum-electrodynamic systems described by the Jaynes-Cummings model. We demonstrate that an effective quadratic coupling between one of the normal modes and the qubit can be induced, and this induced second-order nonlinearity is much larger than that for conventional Kerr-type systems exhibiting photon blockade. Assuming that a coupled normal mode is resonantly driven, we observe that the output fields from the resonators exhibit strong sub-Poissonian photon-number statistics and photon antibunching. Contrary to previous studies on resonant photon blockade, the first-excited state of our device is a pure single-photon Fock state rather than a polariton state, i.e., a highly hybridized qubit-photon state. In addition, it is found that the optical state truncation caused by the strong qubit-induced nonlinearity can lead to an entanglement between the two resonators, even in their steady state under the Markov approximation.

Phonon blockade is a purely quantum phenomenon, analogous to Coulomb and photon blockades, in which a single phonon in an anharmonic mechanical resonator can impede the excitation ofa second phonon. We propose an experimental method to realize phonon blockade in a driven harmonic nanomechanical resonator coupled to a qubit, where the coupling is proportional to the second-order nonlinear susceptibility χ(2). This is in contrast to the standard realizations of phonon and photon blockade effects in Kerr-type χ(3) nonlinear systems. The nonlinear coupling strength can be adjusted conveniently by changing the coherent drive field.As an example, we apply this model to predict and describe phonon blockade in a nanomechanical resonator coupled to a Cooper-pair box (i.e., a charge qubit) with a linear longitudinal coupling. By obtaining the solutions of the steady state for this composite system, we give the conditions forobserving strong antibunching and sub-Poissonian phonon-number statistics in this induced second-order nonlinear system. Besides using the qubit to produce phonon blockade states, the qubit itself can also be employed to detect blockade effects by measuring its states. Numerical simulations indicate that the robustness of the phonon blockade, and the sensitivity of detecting it, will benefit from this strong induced nonlinear coupling.

Electromagnetically induced transparency (EIT) has usually been demonstrated by using three-level atomic systems. In this paper, we theoretically proposed an efficient method to realizeEIT in microwave regime through a coupled system consisting of a flux qubit and a superconducting LC resonator with relatively high quality factor. In the present composed system, the working levels are the dressed states of a two-level flux qubit and the resonators with a probe pump field. There exits a second order coherent transfer between the dressed states. By comparing the results with those in the conventional atomic system we have revealed the physical origin of the EIT phenomenon in this composed system. Since the whole system is artificial and tunable, our scheme may have potential applications in various domains.