Observation of quantum motion of a nanomechanical resonator

In this Letter we use resolved sideband laser cooling to cool a mesoscopic mechanical resonator to near its quantum ground state (phonon occupancy 2.6±0.2), and observe the motional sidebands generated on a second probe laser. Asymmetry in the sideband amplitudes provides a direct measure of the displacement noise power associated with quantum zero-point fluctuations of the nanomechanical resonator, and allows for an intrinsic calibration of the phonon occupation number.     

Basins of attraction of a nonlinear nanomechanical resonator

We present an experiment that systematically probes the basins of attraction of two fixed points of a nonlinear nanomechanical resonator and maps them out with high resolution. We observe a separatrix which progressively alters shape for varying drive strength and changes the relative areas of the two basins of attraction. The observed separatrix is blurred due to ambient fluctuations, including residual noise in the drive system, which cause uncertainty in the preparation of an initial state close to the separatrix. We find a good agreement between the experimentally mapped and theoretically calculated basins of attraction.     

Laser cooling of a nanomechanical resonator mode to its quantum ground state

We show that it is possible to cool a nanomechanical resonator mode to its ground state. The proposed technique is based on resonant laser excitation of a phonon sideband of an embedded quantum dot. The strength of the sideband coupling is determined directly by the difference between the electron-phonon couplings of the initial and final states of the quantum dot optical transition. Possible applications of this scheme include generation of nonclassical states of mechanical motion.     

Engineering quantum decoherence of charge qubit via a nanomechanical resonator

We propose a theoretical scheme to observe the loss of quantum coherence through the coupling of the superconducting charge qubit system to a nanomechanical resonator (NAMR), which has already been successfully fabricated in experiment and is convenient to manipulate. With a similar form to the usual cavity QED system, this qubit-NAMR composite system with engineered coupling exhibits the collapse and revival phenomenon in a progressive decoherence process. Corresponding to the two components of superposition of the two charge eigenstates, the state of the nanomechanical resonator evolves simultaneously towards two distinct quasi-classical states. Therefore the generalized which way detection by the NAMR induces the quantum decoherence of the charge qubit.Received: 21 May 2004, Published online: 9 September 2004PACS: 03.65.-w Quantum mechanics - 74.50. + r Tunneling phenomena; point contacts, weak links, Josephson effects - 03.67.Lx Quantum computation - 85.25.Dq Superconducting quantum interference devices (SQUIDs)     

Tuned transition from quantum to classical for macroscopic quantum states

The boundary between the classical and quantum worlds has been intensely studied. It remains fascinating to explore how far the quantum concept can reach with use of specially fabricated elements. Here we employ a tunable flux qubit with basis states having persistent currents of 1 μA carried by a million pairs of electrons. By tuning the tunnel barrier between these states we see a crossover from quantum to classical. Released from nonequilibrium, the system exhibits spontaneous coherent oscillations. For high barriers the lifetime of the states increases dramatically while the tunneling period approaches the phase coherence time and the oscillations fade away.     

Vacuum Rabi splitting effect in nanomechanical QED system with nonlinear resonator

正Dear Editors,Recently,a nanomechanical resonator with frequency of the order of 1 GHz approaches the quantum regime[1],it is getting closer to test the basic principles of quantum mechanics and very important in the study of quantum information[2].Generally,a nanomechanical QED(qubit-resonator)system consists of a superconducting qubit[3]and a nanomechanical resonator.Increasing the amplitude of oscillating,the nonlinearity of nanomechanical resonator[4]is not negligible which can be exploited to generate nonclassical states in mechanical     

Noise squeezing in a nanomechanical Duffing resonator

We study mechanical amplification and noise squeezing in a nonlinear nanomechanical resonator driven by an intense pump near its dynamical bifurcation point, namely, the onset of Duffing bistability. Phase sensitive amplification is achieved by a homodyne detection scheme, where the displacement detector's output, which has a correlated spectrum around the pump frequency, is down-converted by mixing with a local oscillator operating at the pump frequency with an adjustable phase. The down-converted signal at the mixer's output could be either amplified or deamplified, yielding noise squeezing, depending on the local oscillator phase.     

Noise-enabled precision measurements of a duffing nanomechanical resonator

We report quantitative measurements of the nonlinear response of a radio frequency mechanical resonator with a very high quality factor. We measure the noise-free transitions between the two basins of attraction that appear in the nonlinear regime, and find good agreement with theory. We measure the transition rate response to controlled levels of white noise, and extract the basin activation energy. This allows us to obtain precise values for the relevant frequencies and the cubic nonlinearity in the Duffing oscillator, with applications to parametric sensing.     

Signatures of a noise-induced quantum phase transition in a mesoscopic metal ring

We study a mesoscopic ring with an inline quantum dot threaded by an Aharonov-Bohm flux. Zero-point fluctuations of the electromagnetic environment capacitively coupled to the ring, with omega(s) spectral density, can suppress tunneling through the dot, resulting in a quantum phase transition from an unpolarized to a polarized phase. We show that robust signatures of such a transition can be found in the response of the persistent current in the ring to the external flux as well as to the bias between the dot and the arm. Particular attention is paid to the experimentally relevant cases of Ohmic (s = 1) and sub-Ohmic (s = 1/2) noise.     

Bose-Einstein condensate coupled to a nanomechanical resonator on an atom chip

We theoretically study the coupling of Bose-Einstein condensed atoms to the mechanical oscillations of a nanoscale cantilever with a magnetic tip. This is an experimentally viable hybrid quantum system which allows one to explore the interface of quantum optics and condensed matter physics. We propose an experiment where easily detectable atomic spin flips are induced by the cantilever motion. This can be used to probe thermal oscillations of the cantilever with the atoms. At low cantilever temperatures, as realized in recent experiments, the backaction of the atoms onto the cantilever is significant and the system represents a mechanical analog of cavity quantum electrodynamics. With high but realistic cantilever quality factors, the strong coupling regime can be reached, either with single atoms or collectively with Bose-Einstein condensates. We discuss an implementation on an atom chip.     

Open quantum dots: II. Probing the classical to quantum transition

Open quantum dots provide a natural system in which to study both classical and quantum features of transport. From the classical point of view these dots possess a mixed phase space which yields families of closed, regular orbits as well as an expansive sea of chaos. An important question concerns the manner in which these classical states evolve into the set of quantum states that populate the dot in the quantum limit. In the reverse direction, the manner in which the quantum states evolve to the classical world is governed strongly by Zurek's decoherence theory. This was discussed from the quantum perspective in an earlier review?(Ferry et?al 2011 Semicond. Sci. Technol. 26 043001). Here, we discuss the nature of the various classical states, how they are formed, how they progress to the quantum world, and the signatures that they create in magnetotransport and general conductance studies of these dots.     

Quantum to classical transition in the ground state of a spin-S quantum antiferromagnet

We study a frustrated spin-S staggered-dimer Heisenberg model on square lattice by using the bond-operator representation for quantum spins, and investigate the emergence of classical magnetic order from the quantum mechanical (staggered-dimer singlet) ground state for increasing S. Using triplon analysis, we find the critical couplings for this quantum phase transition to scale as 1 /S(S + 1). We extend the triplon analysis to include the effect of quintet dimer-states, which proves to be essential for establishing the classical order (Néel or collinear in the present study) for large S, both in the purely Heisenberg case and also in the model with single-ion anisotropy.     

Control of sudden transition between classical and quantum correlations of two strongly driven atoms in dissipative cavities

We investigate analytically the dynamics of classical and quantum correlations between two strongly driven atoms, each of which is trapped inside a dissipative cavity. It is found that there exists a finite time interval during which the quantum discord initially prepared in the X-type states is not destroyed by the decay of the cavities. The sudden transition between classical correlation and quantum discord is sensitive to the initial-state parameter, the cavity decay rate, and the cavity mode-driving field detuning. Interestingly, we show that the transition time can be prolonged significantly by increasing the degree of the detuning.     

Spin gases: quantum entanglement driven by classical kinematics

A spin gas is a natural extension of a classical gas. It consists of a large number of particles whose (random) motion is described classically, but, in addition, have internal (quantum mechanical) degrees of freedom that interact during collisions. For specific types of quantum interactions we determine the entanglement that occurs naturally in such systems. We analyze how the evolution of the quantum state is determined by the underlying classical kinematics of the gas. For the Boltzmann gas, we calculate the rate at which entanglement is produced and characterize the entanglement properties of the equilibrium state.     

Diffusive energy growth in classical and quantum driven oscillators

We study the long-time stability of oscillators driven by time-dependent forces originating from dynamical systems with varying degrees of randomness. The asymptotic energy growth is related to ergodic properties of the dynamical system: when the autocorrelation of the force decays sufficiently fast one typically obtains linear diffusive growth of the energy. For a system with good mixing properties we obtain a stronger result in the form of a central limit theorem. If the autocorrelation decays slowly or does not decay, the behavior can depend on subtle properties of the particular model. We study this dependence in detail for a family of quasiperiodic forces. The solution involves the analysis of a small-denominator problem that can be treated by fairly elementary methods. In the special case of a periodic force the quantum stability problem can be expressed in terms of spectral properties of the Floquet operator. In the presence of resonances the spectrum is absolutely continuous. We find explicitly the eigenvalues and eigenfunctions for the nonresonant case.     

A new look at the transition of classical to quantum mechanics

In a recent Rejoinder by Landau,⁽⁸⁾ he indicates that there is an error in a previous article of mine. In fact, this was corrected in an immediately subsequent article⁽²⁾ of mine, and the intriguing problem to which Landau refers is solved in this subsequent article. In the present paper, I consolidate these and other ideas on the subject. In particular, I show that by discussing generalized coordinates in quantum mechanics one achieves much new insight, both philosophical and physical, in understanding the transition of classical to quantum mechanics.     

Enhanced terahertz bistability in a nonlinear Fabry-Perot resonator with n-type quantum wells

The intrinsic bistable terahertz response of intersubband plasmons in wide n-type delta-doped quantum wells is predicted to be enhanced by a resonant Fabry-Perot cavity. With a simple low-Q resonator, the threshold for bistability is decreased by a factor of 2-3 compared with that for bare multiple quantum wells.