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 PACS number(s): 85.85.+j, 42.50.Dv, 73.50.Fq Coherent superposition of states are characteristic traits of quantum mechanics. These phenomena have already been realized in many-particle contexts such as trapped ultracold atoms, 1 superconductors, 2 and photonic systems. 3 A current challenge is to observe these effects for collective degrees of freedom in a macroscopic context in, e.g., mechanical resonators. 4 Recent advances in cooling mechanical resonators and sensitive displacement detection have allowed reaching the motional ground state and observing zero point fluctuations of center of mass. 5,6 Active manipulation and characterization of the quantum state of these systems, as already achieved with photons, 7 seem to be within reach. For a mechanical system, a desirable state to generate is a "cat" state. This is a coherent superposition of two minimum uncertainty wave packets separated by more than their individual quantum fluctuations.For the harmonic oscillator, a minimum uncertainty wave packet is a coherent state |α = exp[αa † − α * a]|0 generated by displacing the oscillator ground state. 8 As shown by Yurke and Stoler, 9 for a nonlinear oscillator H =hω 0n +h n 2 , an initial coherent state |α will after a time t = π/(2 ) evolve into the cat state (1/ √ 2)[e −iπ/4 |α + e iπ/4 |−α ] with the maximum spatial separation = 2|α|.Nanoelectromechanical resonators are typically intrinsically nonlinear. 10 Recent theoretical studies of their quantum dynamics show that it differs from the classical motion 11,12 and the nonlinearity can be exploited in the detection of the quantum signatures. The amplitudes needed to observe nonlinear effects are often orders of magnitude larger than the quantum zero-point fluctuations x 0 = √h /mω 0 . A cat state obtained due to this nonlinearity would have a separation 1. As the decoherence rate scales as 2 (see Refs. 13 and 14), this has, until now, been unfeasible. Instead, coupling to auxiliary quantum systems has been proposed to engineer the nonlinearity. 15,16 We show how, in the limit k B T hω 0 , the intrinsic nonlinearity of a graphene membrane resonator can be used to prepare cat states by applying voltage pulses to local backgates. The reason for using graphene is the ultralow mass of the graphene sheet, which leads to a large x 0 , and an onset of nonlinear response at small amplitudes. 17,18 This implies that cat states with moderate can be constructed without the...

The dissipative quantum dynamics of an anharmonic oscillator is investigated theoretically in the context of carbon-based nano-mechanical systems. In the short-time limit, it is known that macroscopic superposition states appear for such oscillators. In the long-time limit, single-and multiphonon dissipation lead to decoherence of the non-classical states. However, at zero temperature, as a result of two-phonon losses the quantum oscillator eventually evolves into a non-classical steady state. The relaxation of this state due to thermal excitations and one-phonon losses is numerically and analytically studied. The possibility of verifying the occurrence of the non-classical state is investigated and signatures of the quantum features arising in a ring-down setup are presented. The feasibility of the verification scheme is discussed in the context of quantum nano-mechanical systems.

We have studied the nonlinear conductivity of two-dimensional Coulomb glasses. We have used a Monte Carlo algorithm to simulate the dynamic of the system under an applied electric field E. We have compared results for two different models: a regular square lattice with only diagonal disorder and a random array of sites with diagonal and off-diagonal disorder. We have found that for moderate fields the logarithm of the conductivity is proportional to √ E/T 2 , reproducing experimental results. We have also found that in the nonlinear regime the site occupancy in the Coulomb gap follows a Fermi-Dirac distribution with an effective temperature T eff higher than the phonon bath temperature T .

The quantum dynamics of two weakly coupled nonlinear oscillators is analytically and numerically investigated in the context of nonlinear dissipation. The latter facilitates the creation and preservation of non-classical steady states. Starting from a microscopic description of two oscillators individually interacting with their dissipative environments, it is found that in addition to energy relaxation, dephasing arises due to the mutual coupling. Using the negativity as an entanglement measure, it is shown that the coupling entangles the oscillators in the long-time limit. For finite temperatures, entanglement sudden death and rebirth are observed.

We study the asymptotic entanglement of two quantum harmonic oscillators nonlinearly coupled to an environment. Coupling to independent baths and a common bath are investigated. Numerical results obtained using the Wangsness-Bloch-Redfield method are supplemented by analytical results in the rotating wave approximation. The asymptotic negativity as function of temperature, initial squeezing and coupling strength, is compared to results for systems with linear system-reservoir coupling. We find that due to the parity conserving nature of the coupling, the asymptotic entanglement is considerably more robust than for the linearly damped cases. In contrast to linearly damped systems, the asymptotic behavior of entanglement is similar for the two bath configurations in the nonlinearly damped case. This is due to the two-phonon system-bath exchange causing a supression of information exchange between the oscillators via the bath in the common bath configuration at low temperatures.