Trapping and cooling a mirror to its quantum mechanical ground state

We propose a technique aimed at cooling a harmonically oscillating mirror to its quantum mechanical ground state starting from room temperature. Our method, which involves the two-sided irradiation of the vibrating mirror inside an optical cavity, combines several advantages over the two-mirror arrangements being used currently. For comparable parameters the three-mirror configuration provides a stiffer trap for the oscillating mirror. Furthermore, it prevents bistability from limiting the use of higher laser powers for mirror trapping, and also partially does so for mirror cooling. Lastly, it improves the isolation of the mirror from classical noise so that the quantum mechanical dynamics of the mirror become easier to observe. These improvements are expected to bring the task of achieving and detecting ground state occupation for the mirror closer to completion.     

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.     

Signatures for a classical to quantum transition of a driven nonlinear nanomechanical resonator

We seek the first indications that a nanoelectromechanical system (NEMS) is entering the quantum domain as its mass and temperature are decreased. We find them by studying the transition from classical to quantum behavior of a driven nonlinear Duffing resonator. Numerical solutions of the equations of motion, operating in the bistable regime of the resonator, demonstrate that the quantum Wigner function gradually deviates from the corresponding classical phase-space probability density. These clear differences that develop due to nonlinearity can serve as experimental signatures, in the near future, that NEMS resonators are entering the quantum domain.     

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)     

Optomechanically-induced-transparency cooling of massive mechanical resonators to the quantum ground state

Ground state cooling of massive mechanical objects remains a difficult task restricted by the unresolved mechanical sidebands. We propose an optomechanically-induced-transparency cooling scheme to achieve ground state cooling of mechanical motion without the resolved sideband condition in a pure optomechanical system with two mechanical modes coupled to the same optical cavity mode. We show that ground state cooling is achievable for sideband resolution ωm/κ as low as～0.003. This provides a new route for quantum manipulation of massive macroscopic devices and high-precision measurements.     

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.     

Laser resonator supporting a nondiffracting, azimuthally polarized mode

We analyze the lowest-order mode supported by a laser resonator containing an intra-cavity transmissive axicon using the Fox-Li iteration algorithm. Two configurations were considered. By proper choice of the cavity dimensions, the lowest-order mode is nondiffracting and azimuthally polarized. The mode pattern at the output coupler is a Bessel function of the first order.     

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.     

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 resonator with ultrabroad longitudinal mode spacing

A novel type of laser resonator is proposed, in which the resonator length changes with the wavelength of the laser generation. This results in longitudinal mode spacing three orders of magnitude broader than that of conventional cavities. An elementary analysis of the laser resonator is presented and some features and possible applications are discussed.     

Nanomechanical resonator coupling with a double quantum dot: quantum state engineering

We propose a theoretical scheme to realize quantum state engineering of a nanomechanical resonator (NAMR) through the coupling between the NAMR and a double quantum dot (DQD). Hybrid entangled states between the NAMR and the DQD and superposed coherent states of the NAMR are created explicitly. It is shown that quantum state tomography for the NAMR can be implemented through carrying out unitary operations on the NAMR and the DQD. It is indicated that the scheme is feasible at the reach of the present technology.     

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.     

Algorithmic cooling in a momentum state quantum computer

We describe a quantum computer based upon the coherent manipulation of two-level atoms between discrete one-dimensional momentum states. Combinations of short laser pulses with kinetic energy dependent free phase evolution can perform the logical invert, exchange, controlled-NOT, and Hadamard operations on any qubits in the binary representation of the momentum state, as well as conditional phase inversion. These allow a binary right rotation, which halves the momentum distribution in a single coherent process. Fields for the coherent control of atomic momenta may thus be designed as quantum algorithms.     

Small-signal gain of Free Electron Laser in a resonator Gaussian mode

We present an analytical expression for the small-signal gain of a Free Electron Laser (FEL) in the presence of a Gaussian mode. To describe the electron beam evolution we use the one-dimensional (1-d) Vlasov equation. Our perturbation result, valid for small values of the parameterq (length of the undulatorL divided by the Rayleigh rangeZ _R), can be extrapolated to values ofq4÷5.     

Quantization of the Chern invariant polynomial and its topological quantum ground state

The symplectic quantization of the Chern invariant polynomial on a 2n-dimensional manifold is considered. The ground state wave functional as a representation of the vacuum state of the theory is constructed in terms of the Chern-Simons form. An important consequence of these results is that the existence of the Chern-Simons wave functional is not exclusive of topological four-dimensional gauge theory.     

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.     

Laser spot position dependence in photothermal mode cooling of a microcantilever

We explore the laser spot position (LSP) dependence of photothermal mode cooling in a microcantilever-based Fabry-Perot cavity. Experiments on photothermal cooling demonstrate that the direction of photothermal backaction on the first two cantilever modes is LSP dependent, which can be either parallel or antiparallel. A theoretical analysis of this LSP-dependent effect identifies the parallel and the antiparallel coupling regions along the lever. Simulation results are in quantitative agreement with our experimental observations. We conclude that the cooling limit imposed by photothermal mode coupling can be surmounted by operating in the parallel coupling region.     

Cooling of a nanomechanical resonator in presence of a single diatomic molecule

We propose a theoretical scheme for coupling a nanomechanical resonator to a single diatomic molecule via microwave cavity mode of a driven LC$LC$ resonator. We describe the diatomic molecule by a Morse potential and find the corresponding equations of motion of the hybrid system by using Fokker–Planck formalism. Analytical expressions for the effective frequency and the effective damping of the nanomechanical resonator are obtained. We analyze the ground state cooling of the nanomechanical resonator in presence of the diatomic molecule. The results confirm that presence of the molecule improves the cooling process of the mechanical resonator. Finally, the effect of molecule’s parameters on the cooling mechanism is studied.     

On the ground state for quantum graphs

Letters in Mathematical Physics - Ground-state eigenfunctions of Schrödinger operators can often be chosen positive. We analyse to which extent this is true for quantum...