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arXiv:1111.5446 · Physical Review B

Generating macroscopic superposition states in nanomechanical graphene resonators

Aurora Voje, Jari M. Kinaret, Andreas Isacsson

Published May 10, 2012• 26 citations
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Abstract

A theoretical study of the quantum dynamics of a symmetric nanomechanical graphene resonator with degenerate flexural modes is presented. Applying voltage pulses to two back gates, flexural vibrations of the membrane can be selectively actuated and manipulated. For graphene, nonlinear response becomes important for amplitudes comparable to the magnitude of zero-point fluctuations. We show, using analytical and numerical methods, that this allows for creation of catlike superpositions of coherent states as well as superpositions of coherent catlike nonproduct states.

DOI
10.1103/physrevb.85.205415

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A theoretical study of the quantum dynamics of a symmetric nanomechanical graphene resonator with degenerate flexural modes is presented. Applying voltage pulses to two back gates, flexural vibrations of the membrane can be selectively actuated and manipulated. For graphene, nonlinear response becomes important for amplitudes comparable to the magnitude of zero-point fluctuations. We show, using analytical and numerical methods, that this allows for creation of catlike superpositions of coherent states as well as superpositions of coherent catlike nonproduct states.
We propose a hybrid quantum device based on the graphene Josephson junctions, where the vibrational degrees of freedom of a graphene membrane couple to the superconducting circuits. The flexural mode-controlled tunneling of the Cooper pairs introduces a strong and tunable coupling even at the zero-point fluctuations level. By employing this interaction, we show that a parametric process can be efficiently implemented. We then investigate foundational and technological applications of our hybrid device empowered by nonlinear interactions, with fast generation of non-classical mechanical states, and critically enhanced quantum sensing under suitable quantum control. Our work provides the possibility of employing the graphene motional degree of freedom for quantum information processing in circuit quantum nanomechanical structures.
We propose to combine the advantages of graphene, such as easy tunability and long coherence times, with Josephson physics to manufacture qubits. If these qubits are built around a 0 and π\piπ junction they can be controlled by an external flux. Alternatively, a d-wave Josephson junction can itself be tuned via a gate voltage to create superpositions between macroscopically degenerate states. We show that ferromagnets are not required for realizing π\piπ junction in graphene, thus considerably simplifying its physical implementation. We demonstrate how one qubit gates, such as arbitrary phase rotations and the exchange gate, can be implemented.
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 propose a spectroscopic approach to probe tiny vibrations of a nanomechanical resonator (NAMR), which may reveal classical or quantum behavior depending on the decoherence-inducing environment. Our proposal is based on the detection of the voltage-fluctuation spectrum in a superconducting transmission line resonator (TLR), which is indirectly coupled to the NAMR via a controllable Josephson qubit acting as a quantum transducer. The classical (quantum mechanical) vibrations of the NAMR induce symmetric (asymmetric) Stark shifts of the qubit levels, which can be measured by the voltage fluctuations in the TLR. Thus, the motion of the NAMR, including if it is quantum mechanical or not, could be probed by detecting the voltage-fluctuation spectrum of the TLR.
Abstract Sympathetic laser cooling of a single mode graphene membrane coupled to an atomic cloud interacting via Casimir–Polder forces has been recently proposed. Here, we extend this study to the effect of secondary graphene membrane whose frequency may be far or close to resonance. We show that if the two mechanical modes are close together, it is possible to simultaneously cool both modes. Conversely, if the two frequencies are set far apart, the secondary mode does not affect the cooling of the first one. We also study the entanglement properties of the steady-state using the logarithmic negativity. We show how stationary mechanical entanglement between two graphene sheets can be generated by means of vacuum fluctuations. Moreover, we find that, within feasible experimental parameters, large steady-state acoustomechanical entanglement, i.e. entanglement between the phononic and mechanical mode, E N ≈ 5 , can be generated.