We propose the use of a superconducting charge qubit capacitively coupled to two resonant nanomechanical resonators to generate Yurke-Stoler states, i.e., quantum superpositions of pairs of distinguishable coherent states $180\ifmmode^\circ\else\textdegree\fi{}$ out of phase with each other. This is achieved by effectively implementing Kerr nonlinearities induced through the application of a strong external driving field in one of the resonators. A simple study of the effect of dissipation on our scheme is also presented and lower bounds of fidelity and purity of the generated state are calculated. Our procedure to implement a Kerr nonlinearity in this system may be used for high-precision measurements in nanomechanical resonators.
We propose the use of a superconducting charge qubit capacitively coupled to two resonant nanomechanical resonators to generate Yurke-Stoler states, i.e., quantum superpositions of pairs of distinguishable coherent states 180\ifmmode∘\else\textdegree\fi out of phase with each other. This is achieved by effectively implementing Kerr nonlinearities induced through the application of a strong external driving field in one of the resonators. A simple study of the effect of dissipation on our scheme is also presented and lower bounds of fidelity and purity of the generated state are calculated. Our procedure to implement a Kerr nonlinearity in this system may be used for high-precision measurements in nanomechanical resonators.
We propose a scheme for generating squeezed states of a nanomechanical resonator. The scheme is based on a hybrid system consisting of two NAMRs and a superconducting charge qubit (SCCQ). The nonlinear interaction between the two nanomechanical resonators (NAMRs) can be implemented by setting the external biased flux of the SCCQ at some certain values, which plays the role of “nonlinear media”. The noise in the SCCQ does not need to be considered, since we can adiabatically keep the SCCQ at the ground state. In addition, the squeezing parameters can also be adjusted by changing the external driving voltage.
Josephson junctions are a fundamental building block of superconducting quantum circuits. They provide the nonlinearity required to realize quantum bits and enable a wide range of nonlinear phenomena central to quantum technologies. This thesis explores two superconducting systems in which this nonlinearity plays a central role. In the first part, we investigate a superconducting resonator terminated by a superconducting quantum interference device (SQUID), an arrangement of two Josephson junctions connected in parallel. The SQUID provides a tunable Kerr nonlinearity and allows the resonator to be driven parametrically. Under the combined action of the parametric drive, Kerr nonlinearity, and dissipation to the environment, the state of the resonator can undergo abrupt changes as the pump frequency or amplitude is varied. We interpret these changes within the framework of dissipative phase transitions (DPTs). By implementing a finite-component thermodynamic limit, we experimentally and theoretically investigate both first- and second-order DPTs in this system. We characterize their steady-state and dynamical signatures, including squeezing below vacuum, phase coexistence, hysteresis, spontaneous symmetry breaking, and critical slowing down. Finally, we exploit the enhanced susceptibility near the second-order critical point to implement a frequency-estimation protocol. We show that the estimation precision scales quadratically with the effective system size, demonstrating that finite-component DPTs can provide a quantum advantage in a sensing protocol. In the second part, we investigate a novel architecture for the readout of superconducting qubits. Conventional dispersive readout relies on a transverse interaction between a transmon and a resonator, which can lead to Purcell decay and measurement-induced state transitions, ultimately limiting the readout fidelity. To overcome these limitations, we implement a nonlinear coupling by galvanically connecting the transmon and resonator through a Josephson junction. This interaction provides a strong cross-Kerr coupling for clear state discrimination, but also introduces a detrimental transverse interaction. We experimentally show that the exchange part of the transverse interaction can be suppressed by adding a capacitor in parallel with the coupling junction while preserving the strong cross-Kerr coupling. In addition, we show that the same circuit acts as an intrinsic Purcell filter, protecting the qubit against Purcell decay. The coupling junction also induces a Kerr nonlinearity in the resonator, which we exploit to implement a bifurcation readout with a 99.4 % fidelity in a 68 ns integration time. This performance is achieved without a dedicated Purcell filter or a near-quantum-limited amplifier. Overall, this thesis demonstrates the engineering of nonlinear superconducting circuits to investigate dissipative phase transitions, exploit criticality for enhanced quantum sensing, and develop a novel qubit readout architecture enabling fast, high-fidelity measurement.
The coupled dynamics of a nanomechanical resonator and superconducting quantum circuits are studied in three experiments, in the context of studying the quantum limit for force detection and quantum physics of macroscopic objects. In the first experiment, the dispersive mechanical resonance shift from the interaction with a Cooper-pair box qubit is studied. The measured coupling strength is large enough to satisfy one of the conditions required to perform many of the proposed quantum nanomechanical measurements. The resonance shift also probes the microwave-driven response of the qubit, showing Rabi oscillation and Landau-Zener tunneling, proving the coherent dynamics of the qubit. Second, the parametric excitation of nanomechanical motion is studied via experiments with a driven qubit. Degenerate parametric amplification and oscillation are demonstrated, with a new observation of nonlinear dissipation. The squeezing of the back-action noise from the detection amplifier is also observed, up to 4dB. It is the first demonstration using a qubit as an auxiliary system to modify the nanomechanical dynamics, showing a possible route for generation of nanomechanical quantum states. Finally, back-action cooling of nanomechanical motion has been investigated, which is implemented by capacitively coupling a high-Q coplanar waveguide microwave resonator to a nanomechanical resonator. The thermal state with 7.5 mechanical quanta on average is reached, a result that is ultimately limited due to increased bath heating with microwave power. The heating is consistent with a model based on two-level systems resonantly coupled to the nanomechanical mode. This additional heating suggests future efforts to improve coupling and for reducing two-level system density in materials employed to reach the motional ground state via back-action cooling.
We describe a possible implementation of the nanomechanical quantum superposition generation and detection scheme described in the preceding, companion paper (Armour A D and Blencowe M P 2008 New. J. Phys. 10 095004). The implementation is based on the circuit quantum electrodynamics (QED) set-up, with the addition of a mechanical degree of freedom formed out of a suspended, doubly-clamped segment of the superconducting loop of a dc SQUID located directly opposite the centre conductor of a coplanar waveguide (CPW). The relative merits of two SQUID based qubit realizations are addressed, in particular a capacitively coupled charge qubit and inductively coupled flux qubit. It is found that both realizations are equally promising, with comparable qubit–mechanical resonator mode as well as qubit–microwave resonator mode coupling strengths.
We propose a scheme for generating squeezed states based on a superconducting hybrid system. Our system consists of a nanomechanical resonator, a superconducting flux qubit, and a superconducting transmission line resonator. Using our proposal, one can easily generate the squeezed states of the nanomechanical resonator. In our scheme, the nonlinear interaction between the nanomechanical resonator and the superconducting transmission line resonator can be implemented by the flux qubit as 'nonlinear media' with a tunable Josephson energy. The realization of the nonlinearity does not need any operations on the flux qubit and just needs to adiabatically keep it at the ground state, which can greatly decrease the effect of the decoherence of the flux qubit on the squeezed efficiency.
We investigate nonlinear effects in an electromechanical system involving a superconducting charge qubit coupled to transmission line resonator and a nanomechanical oscillator, which in turn is coupled to another transmission line resonator. The nonlinearities induced by the superconducting qubit and the optomechanical coupling play an important role in generating optomechanical entanglement as well as the squeezing of the transmitted microwave field. We show that strong squeezing of the microwave field and robust optomechanical entanglement can be achieved in the presence of moderate thermal decoherence. We also discuss the effect of the coupling of the superconducting qubit to the nanomechanical oscillator on the bistability behaviour of the mean photon number.