Qubit-assisted thermometry of a quantum harmonic oscillator

We use the theory of quantum estimation in two different qubit-boson coupling models to demonstrate that the temperature of a quantum harmonic oscillator can be estimated with high precision by quantum-limited measurements on the qubit. The two models that we address embody situations of current physical interest due to their connection with ongoing experimental efforts on the control of mesoscopic dynamics. We show that population measurements performed over the qubit probe are near optimal for a broad range of temperatures of the harmonic oscillator.

Distillable entanglement and area laws in spin and harmonic-oscillator systems

We address the presence of nondistillable (bound) entanglement in natural many-body systems. In particular, we consider standard harmonic and spin-1/2 chains, at thermal equilibrium and characterized by few interaction parameters. The existence of bound entanglement is addressed by calculating explicitly the negativity of entanglement for different partitions. This allows us to individuate a range of temperatures for which no entanglement can be distilled by means of local operations, despite the system being globally entangled. We discuss how the appearance of bound entanglement can be linked to entanglement-area laws, typical of these systems. Various types of interactions are explored, showing that the presence of bound entanglement is an intrinsic feature of these systems. In the harmonic case, we analytically prove that thermal bound entanglement persists for systems composed by an arbitrary number of particles. Our results strongly suggest the existence of bound entangled states in the macroscopic limit also for spin-1/2 systems.

Thermodynamics of trajectories of a quantum harmonic oscillator coupled to N baths

We undertake a thorough analysis of the thermodynamics of the trajectories followed by a quantum harmonic oscillator coupled to $N$ dissipative baths by using a new approach to large-deviation theory inspired by phase-space quantum optics. As an illustrative example, we study the archetypal case of a harmonic oscillator coupled to two thermal baths, allowing for a comparison with the analogous classical result. In the low-temperature limit, we find a significant quantum suppression in the rate of work exchanged between the system and each bath. We further show how the presented method is capable of giving analytical results even for the case of a driven harmonic oscillator. Based on that result, we analyse the laser cooling of the motion of a trapped ion or optomechanical system, illustrating how the emission statistics can be controllably altered by the driving force.

ESTIMATION OF PURITY FOR A QUANTUM HARMONIC OSCILLATOR INITIALLY PREPARED IN A DISPLACED THERMAL STATE

We address the estimation of purity for a quantum oscillator initially prepared in a displaced thermal state and probed by a suitably prepared qubit interacting with the oscillator via Jaynes-Cummings Hamiltonian without the rotating-wave approximation. We evaluate the quantum Fisher information (QFI) and show that optimal estimation of purity can be achieved by measuring the population of the qubit after a properly chosen interaction time. We also address the estimation of purity at fixed total energy and show that the corresponding precision is independent of the presence of a coherent amplitude.

Heat transport in harmonic oscillator systems with thermal baths: application to optomechanical arrays

We investigate the transport of phonons between N harmonic oscillators in contact with independent thermal baths and coupled to a common oscillator, and derive an expression for the steady state heat flow between the oscillators in the weak coupling limit. We apply these results to an optomechanical array consisting of a pair of mechanical resonators coupled to a single quantized electromagnetic field mode by radiation pressure as well as to thermal baths with different temperatures. In the weak coupling limit this system is shown to be equivalent to two mutually-coupled harmonic oscillators in contact with an effective common thermal bath in addition to their independent baths. The steady state occupation numbers and heat flows are derived and discussed in various regimes of interest.

Analytical calculation of far infrared spectra of ice in terms of a molecular model

Wideband far infrared (FIR) spectra of complex permittivity e(p) of ice are calculated in terms of a simple analytical theory based on the method of dipolar autocorrelation functions. The molecular model represents a revision of the model recently presented for liquid water in Adv. Chem. Phys. 127 (2003) 65. A composite two-fractional model is proposed. The model is characterised by three phenomenological potential wells corresponding to the three FIR bands observed in ice. The first fraction comprises dipoles reorienting in a rather narrow and deep hat-like well; these dipoles generate the librational band centred at the frequency approximate to 880 cm(-1). The second fraction comprises elastically interacting particles; they generate two nearby bands placed around frequency 200 cm(-1). For description of one of these bands the harmonic oscillator (HO) model is used, in which translational oscillations of two charged molecules along the H-bond are considered. The other band is produced by the H-bond stretch, which governs hindered rotation of a rigid dipole. Such a motion and its dielectric response are described in terms of a new cut parabolic (CP) model applicable for any vibration amplitude. The composite hat-HO-CP model results in a smooth epsilon(nu) ice spectrum, which does not resemble the noise-like spectra of ice met in the known literature. The proposed theory satisfactorily agrees with the experimental ice spectrum measured at - 7 degrees C. The calculated longitudinal optic-transverse optic (LO-TO) splitting occurring at approximate to 250 cm(-1) qualitatively agrees with the measured data. (c) 2004 Elsevier B.V. All rights reserved.

Geometric-phase backaction in a mesoscopic qubit-oscillator system

We illustrate a reverse Von Neumann measurement scheme in which a geometric phase induced on a quantum harmonic oscillator is measured using a microscopic qubit as a probe. We show how such a phase, generated by a cyclic evolution in the phase space of the harmonic oscillator, can be kicked back on the qubit, which plays the role of a quantum interferometer. We also extend our study to finite-temperature dissipative Markovian dynamics and discuss potential implementations in micro-and nanomechanical devices coupled to an effective two-level system.

Generalized Langevin equation: An efficient approach to nonequilibrium molecular dynamics of open systems

The generalized Langevin equation (GLE) has been recently suggested to simulate the time evolution of classical solid and molecular systems when considering general nonequilibrium processes. In this approach, a part of the whole system (an open system), which interacts and exchanges energy with its dissipative environment, is studied. Because the GLE is derived by projecting out exactly the harmonic environment, the coupling to it is realistic, while the equations of motion are non-Markovian. Although the GLE formalism has already found promising applications, e. g., in nanotribology and as a powerful thermostat for equilibration in classical molecular dynamics simulations, efficient algorithms to solve the GLE for realistic memory kernels are highly nontrivial, especially if the memory kernels decay nonexponentially. This is due to the fact that one has to generate a colored noise and take account of the memory effects in a consistent manner. In this paper, we present a simple, yet efficient, algorithm for solving the GLE for practical memory kernels and we demonstrate its capability for the exactly solvable case of a harmonic oscillator coupled to a Debye bath.

Disturbance attenuation in linear systems via dynamical compensators: A parametric eigenstructure assignment approach

A simple approach is proposed for disturbance attenuation in multivariable linear systems via dynamical output compensators based on complete parametric eigenstructure assignment. The basic idea is to minimise the H-2 norm of the disturbance-output transfer function using the design freedom provided by eigenstructure assignment. For robustness, the closed-loop system is restricted to be nondefective. Besides the design parameters, the closed-loop eigenvalues are also optimised within desired regions on the left-half complex plane to ensure both closed-loop stability and dynamical performance. With the proposed approach, additional closed-loop specifications can be easily achieved. As a demonstration, robust pole assignment, in the sense that the closed-loop eigenvalues are as insensitive as possible to open-loop system parameter perturbations, is treated. Application of the proposed approach to robust control of a magnetic bearing with a pair of opposing electromagnets and a rigid rotor is discussed.

Thermal bound entanglement in macroscopic systems and area law

Does bound entanglement naturally appear in quantum many-body systems? We address this question by showing the existence of bound-entangled thermal states for harmonic oscillator systems consisting of an arbitrary number of particles. By explicit calculations of the negativity for different partitions, we find a range of temperatures for which no entanglement can be distilled by means of local operations, despite the system being globally entangled. We offer an interpretation of this result in terms of entanglement-area laws, typical of these systems. Finally, we discuss generalizations of this result to other systems, including spin chains.

More bang for your buck: Super-adiabatic quantum engines

The practical untenability of the quasi-static assumption makes any realistic engine intrinsically irreversible and its operating time finite, thus implying friction effects at short cycle times. An important technological goal is thus the design of maximally efficient engines working at the maximum possible power. We show that, by utilising shortcuts to adiabaticity in a quantum engine cycle, one can engineer a thermodynamic cycle working at finite power and zero friction. Our findings are illustrated using a harmonic oscillator undergoing a quantum Otto cycle.

Discrete-Time Conserved Quantities for Damped Oscillators

Numerical sound synthesis is often carried out using the finite difference time domain method. In order to analyse the stability of the derived models, energy methods can be used for both linear and nonlinear settings. For Hamiltonian systems the existence of a conserved numerical energy-like quantity can be used to guarantee the stability of the simulations. In this paper it is shown how to derive similar discrete conservation laws in cases where energy is dissipated due to friction or in the presence of an energy source due to an external force. A damped harmonic oscillator (for which an analytic solution is available) is used to present the proposed methodology. After showing how to arrive at a conserved quantity, the simulation of a nonlinear single reed shows an example of an application in the context of musical acoustics.

Entanglement between collective operators in a linear harmonic chain

We investigate entanglement between collective operators of two blocks of oscillators in an infinite linear harmonic chain. These operators are defined as averages over local operators (individual oscillators) in the blocks. On the one hand, this approach of "physical blocks" meets realistic experimental conditions, where measurement apparatuses do not interact with single oscillators but rather with a whole bunch of them, i.e., where in contrast to usually studied "mathematical blocks" not every possible measurement is allowed. On the other, this formalism naturally allows the generalization to blocks which may consist of several noncontiguous regions. We quantify entanglement between the collective operators by a measure based on the Peres-Horodecki criterion and show how it can be extracted and transferred to two qubits. Entanglement between two blocks is found even in the case where none of the oscillators from one block is entangled with an oscillator from the other, showing genuine bipartite entanglement between collective operators. Allowing the blocks to consist of a periodic sequence of subblocks, we verify that entanglement scales at most with the total boundary region. We also apply the approach of collective operators to scalar quantum field theory.

Entanglement generation in harmonic chains: Tagging by squeezing

We address the problem of springlike coupling between bosons in an open-chain configuration where the counter-rotating terms are explicitly included. We show that fruitful insight can be gained by decomposing the time-evolution operator of this problem into a pattern of linear-optics elements. This allows us to provide a clear picture of the effects of the counter-rotating terms in the important problem of long-haul entanglement distribution. The analytic control over the variance matrix of the state of the bosonic register allows us to track the dynamics of the entanglement. This helps in designing a global addressing scheme, complemented by a proper initialization of the register, which quantitatively improves the entanglement between the extremal oscillators in the chain, thus providing a strategy for feasible long-distance entanglement distribution.

High harmonic generation by halogen anions and noble gas atoms in a laser field

A comparative study of high harmonic generation (HHG) by atoms and ions with active p-electrons is carried out in the theoretical framework of the rescattering mechanism. The substate with m(l) = 0, i.e. zero orbital momentum projection along the electric vector of a linearly polarized laser wave, is found to give the major contribution to the HHG rate. Our calculations for HHG by an H atom in an excited 2p-state demonstrate that the rate for recombination into a final state with a different value of m(l) (= +/- 1), is higher for lower harmonic orders N, while for higher N (beyond the plateau domain) the difference vanishes. For species with closed electron shells, the m(l)-changing transitions are forbidden by the Pauli exclusion principle. We report absolute HHG rates for halogen ions and noble gas atoms at various intensities. These results demonstrate that the Coulomb binding potential of the atoms considerably enhances both the ionization and recombination steps in the rescattering process. However, the weak binding energy of the anions allows lower orders of HHG to be efficiently produced at relatively low intensities, from which we conclude that observation of HHG by an anion is experimentally feasible.