arXiv subjects

G. J. Milburn

Publications and source records attributed to G. J. Milburn.

At least 55 records · Page 3Linked to original sources

arXiv2011

Phonon number quantum jumps in an optomechanical system

We describe an optomechanical system in which the mean phonon number of a single mechanical mode conditionally displaces the amplitude of the optical field. Using homodyne detection of the output field we establish the conditions under which phonon number quantum jumps can be inferred from the measurement record: both the cavity damping rate and the measurement rate of the phonon number must be much greater than the thermalization rate of the mechanical mode. We present simulations of the conditional dynamics of the measured system using the stochastic master equation. In the good-measurement limit, the conditional evolution of the mean phonon number shows quantum jumps as phonons enter and exit the mechanical resonator via the bath.

quant-ph↗

arXiv2010

Quantum entanglement between a nonlinear nanomechanical resonator and a microwave field

We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semi-classical approximation of this system has an interesting fixed point bifurcation structure. In the semi-classical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positive to negative detuning. We show that signatures of this bifurcation structure are also present in the full dissipative quantum system and further show that it leads to mixed state entanglement between the nanomechanical resonator and the microwave cavity in the dissipative quantum system that is a maximum close to the semi-classical bifurcation. Quantum signatures of the semi-classical limit-cycles are presented.

cond-mat.mes-hall↗

arXiv2010

Linear amplification and quantum cloning for non-Gaussian continuous variables

We investigate phase-insensitive linear amplification at the quantum limit for single- and two-mode states and show that there exists a broad class of non-Gaussian states whose nonclassicality survives even at an arbitrarily large gain. We identify the corresponding observable nonclassical effects and find that they include, remarkably, two-mode entanglement. The implications of our results for quantum cloning outside the Gaussian regime are also addressed.

quant-ph↗

arXiv2010

Vibration-enhanced quantum transport

In this paper, we study the role of collective vibrational motion in the phenomenon of electronic energy transfer (EET) along a chain of coupled electronic dipoles with varying excitation frequencies. Previous experimental work on EET in conjugated polymer samples has suggested that the common structural framework of the macromolecule introduces correlations in the energy gap fluctuations which cause coherent EET. Inspired by these results, we present a simple model in which a driven nanomechanical resonator mode modulates the excitation energy of coupled quantum dots and find that this can indeed lead to an enhancement in the transport of excitations across the quantum network. Disorder of the on-site energies is a key requirement for this to occur. We also show that in this solid state system phase information is partially retained in the transfer process, as experimentally demonstrated in conjugated polymer samples. Consequently, this mechanism of vibration enhanced quantum transport might find applications in quantum information transfer of qubit states or entanglement.

quant-ph↗

arXiv2010

Continuous quantum non-demolition measurement of Fock states of a nanoresonator using feedback-controlled circuit QED

We propose a scheme for the quantum non-demolition (QND) measurement of Fock states of a nanomechanical resonator via feedback control of a coupled circuit QED system. A Cooper pair box (CPB) is coupled to both the nanoresonator and microwave cavity. The CPB is read-out via homodyne detection on the cavity and feedback control is used to effect a non-dissipative measurement of the CPB. This realizes an indirect QND measurement of the nanoresonator via a second-order coupling of the CPB to the nanoresonator number operator. The phonon number of the Fock state may be determined by integrating the stochastic master equation derived, or by processing of the measurement signal.

quant-ph↗

arXiv2010

Single-photon optomechanics in the strong coupling regime

We give a theoretical description of a coherently driven opto-mechanical system with a single added photon. The photon source is modeled as a cavity which initially contains one photon and which is irreversibly coupled to the opto-mechanical system. We show that the probability for the additional photon to be emitted by the opto-mechanical cavity will exhibit oscillations under a Lorentzian envelope, when the driven interaction with the mechanical resonator is strong enough. Our scheme provides a feasible route towards quantum state transfer between optical photons and micromechanical resonators.

quant-ph↗

arXiv2009

Intracavity weak nonlinear phase shifts with single photon driving

We investigate a doubly resonant optical cavity containing a Kerr nonlinear medium that couples two modes by a cross phase modulation. One of these modes is driven by a single photon pulsed field, and the other mode is driven by a coherent state. We find an intrinsic phase noise mechanism for the cross phase shift on the coherent beam which can be attributed to the random emission times of single photons from the cavity. An application to a weak nonlinearity phase gate is discussed.

quant-ph↗

arXiv2009

Kerr nonlinearities and nonclassical states with superconducting qubits and nanomechanical resonators

We propose the use of a superconducting charge qubit capacitively coupled to two resonant nanomechanical resonators to generate Yurke-Stoler states, i.e. quantum superpositions of pairs of distinguishable coherent states 180$^\circ$ out of phase with each other. This is achieved by effectively implementing Kerr nonlinearities induced through application of a strong external driving field in one of the resonators. A simple study of the effect of dissipation on our scheme is also presented, and lower bounds of fidelity and purity of the generated state are calculated. Our procedure to implement a Kerr nonlinearity in this system may be used for high precision measurements in nanomechanical resonators.

quant-ph↗

arXiv2008

$χ^{(3)}$ non-Gaussian state generation for light using a trapped ion

According to the Gottesmann-Knill theorem the non-Gaussian states are necessary component for a nontrivial quantum computation. We show two efficient and deterministic methods of $χ^{(3)}$ non-Gaussian state generation for a cavity mode using a single trapped ion. Both require ion motional state transfer to the cavity field. The methods are experimentally feasible. The first is based on the well-known protocol for an ion finite motional superposition state generation. It allows for an arbitrary good approximation of $χ^{(3)}$ non-Gaussian states. We give criteria based on the Wigner function which quantify the error resulting from the approximation. The second and novel method enables an exact non-Gaussian state generation using one laser pulse only.

quant-ph↗

arXiv2008

Nanomechanical squeezing with detection via a microwave cavity

We study a parametrically-driven nanomechanical resonator capacitively coupled to a microwave cavity. If the nanoresonator can be cooled to near its quantum ground state then quantum squeezing of a quadrature of the nanoresonator motion becomes feasible. We consider the adiabatic limit in which the cavity mode is slaved to the nanoresonator mode. By driving the cavity on its red-detuned sideband, the squeezing can be coupled into the microwave field at the cavity resonance. The red-detuned sideband drive is also compatible with the goal of ground state cooling. Squeezing of the output microwave field may be inferred using a technique similar to that used to infer squeezing of the field produced by a Josephson parametric amplifier, and subsequently, squeezing of the nanoresonator motion may be inferred. We have calculated the output field microwave squeezing spectra and related this to squeezing of the nanoresonator motion, both at zero and finite temperature. Driving the cavity on the blue-detuned sideband, and on both the blue and red sidebands, have also been considered within the same formalism.

quant-ph↗

arXiv2008

Quantum Connectivity of Space-Time and Gravitationally Induced Decorrelation of Entanglement

We discuss an alternative formulation of the problem of quantum optical fields in a curved space-time using localized operators. We contrast the new formulation with the standard approach and find observable differences for entangled states. We propose an experiment in which an entangled pair of optical pulses are propagated through non-uniform gravitational fields and find that the new formulation predicts de-correlation of the optical entanglement under experimentally realistic conditions.

quant-ph↗

arXiv2008

Noise in an SSET-resonator driven by an external field

We investigate the noise properties of a superconducting single electron transistor (SSET) coupled to an harmonically driven resonator. Using a Langevin equation approach, we calculate the frequency spectrum of the SSET charge and calculate its effect on the resonator field. We find that the heights of the peaks in the frequency spectra depend sensitively on the amplitude of the resonator oscillation and hence suggest that the heights of these peaks could act as a sensitive signal for detecting the small changes in the amplitude of the drive. The previously known results for the effective amplitude-dependent damping and temperature provided by the SSET for the case of a low frequency resonator are generalized for all resonator frequencies.

cond-mat.mes-hall↗

arXiv2008

Spatial correlation functions for the collective degrees of freedom of many trapped ions

Spatial correlation functions provide a glimpse into the quantum correlations within a quantum system. Ions in a linear trap collectively form a nonuniform, discretized background on which a scalar field of phonons propagates. Trapped ions have the experimental advantage of each having their own "built-in" motional detector: electronic states that can be coupled, via an external laser, to the ion's vibrational motion. The post-interaction electronic state can be read out with high efficiency, giving a stochastic measurement record whose classical correlations reflect the quantum correlations of the ions' collective vibrational state. Here we calculate this general result, then we discuss the long detection-time limit and specialize to Gaussian states, and finally we compare the results for thermal versus squeezed states.

quant-ph↗

arXiv2008

Wigner Function Evolution of Quantum States in Presence of Self-Kerr Interaction

A Fokker-Planck equation for the Wigner function evolution in a noisy Kerr medium ($χ^{(3)}$ non-linearity) is presented. We numerically solved this equation taking a coherent state as an initial condition. The dissipation effects are discussed. We provide examples of quantum interference, sub-Planck phase space structures, and Gaussian versus non-Gaussian dynamical evolution of the state. The results also apply to the description of a nanomechanical resonator with an intrinsic Duffing nonlinearity.

quant-ph↗

arXiv2008

Nonlinear quantum metrology using coupled nanomechanical resonators

We consider a nanomechanical analogue of a nonlinear interferometer, consisting of two parallel, flexural nanomechanical resonators, each with an intrinsic Duffing nonlinearity and with a switchable beamsplitter-like coupling between them. We calculate the precision with which the strength of the nonlinearity can be estimated and show that it scales as $1/n^{3/2}$, where $n$ is the mean phonon number of the initial state. This result holds even in the presence of dissipation, but assumes the ability to make measurements of the quadrature components of the nanoresonators.

quant-ph↗

arXiv2008

Quantum noise in a nano mechanical Duffing resonator

We determine the small signal gain and noise response of an amplifier based on the nonlinear response of a quantum nanomechanical resonator. The resonator is biased in the nonlinear regime by a strong harmonic bias force and we determine the response to a small additional driving signal detuned with respect to the bias force.

quant-ph↗

arXiv2007

Iterated dynamical maps in an ion trap

Iterated dynamical maps offer an ideal setting to investigate quantum dynamical bifurcations and are well adapted to few-qubit quantum computer realisations. We show that a single trapped ion, subject to periodic impulsive forces, exhibits a rich structure of dynamical bifurcations derived from the Jahn-Teller Hamiltonian flow model. We show that the entanglement between the oscillator and electronic degrees of freedom reflects the underlying dynamical bifurcation in a Floquet eigenstate.

quant-ph↗

arXiv2007

Entangling a nanomechanical resonator and a superconducting microwave cavity

We propose a scheme able to entangle at the steady state a nanomechanical resonator with a microwave cavity mode of a driven superconducting coplanar waveguide. The nanomechanical resonator is capacitively coupled with the central conductor of the waveguide and stationary entanglement is achievable up to temperatures of tens of milliKelvin.

cond-mat.mes-hall↗