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Register a new userProbing the quantum coherence of a nanomechanical resonator using a superconducting qubit: I. Echo scheme
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We propose a scheme in which the quantum coherence of a nanomechanical resonator can be probed using a superconducting qubit. We consider a mechanical resonator coupled capacitively to a Cooper-pair box and assume that the superconducting qubit is tuned to the degeneracy point so that its coherence time is maximised and the electro-mechanical coupling can be approximated by a dispersive Hamiltonian. When the qubit is prepared in a superposition of states this drives the mechanical resonator progressively into a superposition which in turn leads to apparent decoherence of the qubit. Applying a suitable control pulse to the qubit allows its population to be inverted resulting in a reversal of the resonator dynamics. However, the resonators interactions with its environment mean that the dynamics is not completely reversible. We show that this irreversibility is largely due to the decoherence of the mechanical resonator and can be inferred from appropriate measurements on the qubit alone. Using estimates for the parameters involved based on a specific realization of the system we show that it should be possible to carry out this scheme with existing device technology.
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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. Submitted]. 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.
Metamaterial resonant structures made from arrays of superconducting lumped circuit elements can exhibit microwave mode spectra with left-handed dispersion, resulting in a high density of modes in the same frequency range where superconducting qubits are typically operated, as well as a bandgap at lower frequencies that extends down to dc. Using this novel regime for multi-mode circuit quantum electrodynamics, we have performed a series of measurements of such a superconducting metamaterial resonator coupled to a flux-tunable transmon qubit. Through microwave measurements of the metamaterial, we have observed the coupling of the qubit to each of the modes that it passes through. Using a separate readout resonator, we have probed the qubit dispersively and characterized the qubit energy relaxation as a function of frequency, which is strongly affected by the Purcell effect in the presence of the dense mode spectrum. Additionally, we have investigated the ac Stark shift of the qubit as the photon number in the various metamaterial modes is varied. The ability to tailor the dense mode spectrum through the choice of circuit parameters and manipulate the photonic state of the metamaterial through interactions with qubits makes this a promising platform for analog quantum simulation and quantum memories.
Phonon modes at microwave frequencies can be cooled to their quantum ground state using conventional cryogenic refrigeration, providing a convenient way to study and manipulate quantum states at the single phonon level. Phonons are of particular interest because mechanical deformations can mediate interactions with a wide range of different quantum systems, including solid-state defects, superconducting qubits, as well as optical photons when using optomechanically-active constructs. Phonons thus hold promise for quantum-focused applications as diverse as sensing, information processing, and communication. Here, we describe a piezoelectric quantum bulk acoustic resonator (QBAR) with a 4.88 GHz resonant frequency that at cryogenic temperatures displays large electromechanical coupling strength combined with a high intrinsic mechanical quality factor $Q_i approx 4.3 times 10^4$. Using a recently-developed flip-chip technique, we couple this QBAR resonator to a superconducting qubit on a separate die and demonstrate quantum control of the mechanics in the coupled system. This approach promises a facile and flexible experimental approach to quantum acoustics and hybrid quantum systems.
We demonstrate high-contrast state detection of a superconducting flux qubit. Detection is realized by probing the microwave transmission of a nonlinear resonator, based on a SQUID. Depending on the driving strength of the resonator, the detector can be operated in the monostable or the bistable mode. The bistable operation combines high-sensitivity with intrinsic latching. The measured contrast of Rabi oscillations is as high as 87 %; of the missing 13 %, only 3 % is unaccounted for. Experiments involving two consecutive detection pulses are consistent with preparation of the qubit state by the first measurement.
We present an analysis of the dynamics of a nanomechanical resonator coupled to a superconducting single electron transistor (SSET) in the vicinity of the Josephson quasiparticle (JQP) and double Josephson quasiparticle (DJQP) resonances. For weak coupling and wide separation of dynamical timescales, we find that for either superconducting resonance the dynamics of the resonator is given by a Fokker-Planck equation, i.e., the SSET behaves effectively as an equilibrium heat bath, characterised by an effective temperature, which also damps the resonator and renormalizes its frequency. Depending on the gate and drain-source voltage bias points with respect to the superconducting resonance, the SSET can also give rise to an instability in the mechanical resonator marked by negative damping and temperature within the appropriate Fokker-Planck equation. Furthermore, sufficiently close to a resonance, we find that the Fokker-Planck description breaks down. We also point out that there is a close analogy between coupling a nanomechanical resonator to a SSET in the vicinity of the JQP resonance and Doppler cooling of atoms by means of lasers.
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