James Cresser

• PhD
• Research Associate at University of Glasgow

We investigate the effects of the electromagnetic vacuum field on a harmonically bound electron. We show that in the electric-dipole approximation the model atom couples only to an effective one-dimensional electric field. In a simplified form, in which the problem is reduced to a single spatial dimension, we determine, analytically, the form of th...

The spin-boson model usually considers a spin coupled to a single bosonic bath. However, some physical situations require coupling of the spin to multiple environments. For example, spins interacting with phonons in three-dimensional magnetic materials. Here, we consider a spin coupled isotropically to three independent baths. We show that coupling...

The equilibrium properties of nanoscale systems can deviate significantly from standard thermodynamics due to their coupling to an environment. We investigate this here for the θ-angled spin–boson model, where we first derive a compact and general form of the classical equilibrium state including environmental corrections to all orders. Secondly, f...

We reanalyse the quantum damped harmonic oscillator, introducing three less than common features. These are (i) the use of a continuum model of the reservoir rather than an ensemble of discrete oscillators, (ii) an exact diagonalisation of the Hamiltonian by adapting a technique pioneered by Fano, and (iii) the use of the thermofield technique for d...

We reanalyse the quantum damped harmonic oscillator, introducing three less than common features. These are (i) the use of a continuum model of the reservoir rather than an ensemble of discrete oscillators, (ii) an exact diagonalisation of the Hamiltonian by adapting a technique pioneered by Fano, and (iii) the use of the thermofield technique for...

The spin-boson model usually considers a spin coupled to a single bosonic bath. However, some physical situations require coupling of the spin to multiple environments. For example, spins interacting with phonons in three-dimensional magnetic materials. Here, we consider a spin coupled isotropically to three independent baths. We show that coupling...

It is known that the equilibrium properties of nanoscale systems can deviate significantly from standard thermodynamics due to their coupling to an environment. For the generalized $\theta$-angled spin-boson model, here we derive an explicit form of the classical mean force equilibrium state. Taking the large spin limit of the quantum spin-boson mo...

The dynamical convergence of a system to the thermal distribution, or Gibbs state, is a standard assumption across all of the physical sciences. The Gibbs state is determined just by temperature and energies of the system. However, at decreasing system sizes, i.e., for nanoscale and quantum systems, the interaction with their environments is not ne...

The Gibbs state is widely taken to be the equilibrium state of a system in contact with an environment at temperature T. However, non-negligible interactions between system and environment can give rise to an altered state. Here, we derive general expressions for this mean force Gibbs state, valid for any system that interacts with a bosonic reserv...

The dynamical convergence of a system to the thermal distribution, or Gibbs state, is a standard assumption across all of the physical sciences. The Gibbs state is determined just by temperature and the system's energies alone. But at decreasing system sizes, i.e. for nanoscale and quantum systems, the interaction with their environments is not neg...

The Gibbs state is widely taken to be the equilibrium state of a system in contact with an environment at temperature $T$. However, non-negligible interactions between system and environment can give rise to an altered state. Here we derive general expressions for this mean force Gibbs state, valid for any system that interacts with a bosonic reser...

The micromaser is examined with the aim of understanding certain of its properties based on a time-reversed quantum trajectory analysis. The background theory of master equations derived from a repeated interaction model perspective is briefly reviewed and extended by taking into account the more general renewal process description of the sequence...

Time-reversed quantum trajectories are defined for a thermally pumped micromaser for atom arrivals modelled as a renewal process. They are shown to arise naturally in the derivation of an equality between atomic beam and cavity field correlations, and are used to obtain Crooks fluctuation relations for entropy flow.

The micromaser is examined with the aim of understanding certain of its properties based on a time-reversed quantum trajectory analysis. The background theory of master equations derived from a repeated interaction model perspective is briefly reviewed and extended by taking into account the more general renewal process description of the sequence...

The coarse-graining approach to deriving the quantum Markovian master equation is revisited, with close attention given to the underlying approximations. It is further argued that the time interval over which the coarse-graining is performed is a free parameter that can be given a physical measurement-based interpretation. In the case of the dampin...

We analyse the properties of a strongly-damped quantum harmonic oscillator by means of an exact diagonalisation of the full Hamiltonian, including both the oscillator and the reservoir degrees of freedom to which it is coupled. Many of the properties of the oscillator, including its steady-state properties and entanglement with the reservoir can be...

We investigate how to model Markovian evolution of coupled harmonic oscillators, each of them interacting with a local environment. When the coupling between the oscillators is weak, dissipation may be modeled using local Lindblad terms for each of the oscillators in the master equation, as is commonly done. When the coupling between oscillators is...

Quantum random walks have received much attention for their intrinsic interest and many possible uses and have been experimentally demonstrated. In this work we look at the possibility of using a biased one-dimensional (1D) quantum walk as an element within a larger quantum device. We ask whether one can use a quantum walk to act as a router with o...

Master equations govern the time evolution of a quantum system interacting with an environment, and may be written in a variety of forms. Time-independent or memoryless master equations, in particular, can be cast in the well-known Lindblad form. Any time-local master equation, Markovian or non-Markovian, may in fact also be written in a Lindblad-l...

Buschʼs theorem deriving the standard quantum probability rule can be regarded as a more general form of Gleasonʼs theorem. Here we show that a further generalization is possible by reducing the number of quantum postulates used by Busch. We do not assume that the positive measurement outcome operators are effects or that they form a probability op...

We show that Gleason's theorem, in the form recently generalised by Busch, may be further simplified by dropping one of the three properties from which it was derived. The result is a more general probability than that usually employed in quantum theory in that it shows that any set of positive operators can represent the probabilities for a set of...

We analyze the dynamics of various kinds of correlations present between two initially entangled independent qubits, each one subject to a local phase-noisy laser. We give explicit expressions for the relevant quantifiers of correlations for the general case of single-qubit unital evolution, which includes the case of a phase-noisy laser. Although...

We consider two recently proposed measures of non-Markovianity applied to a particular quantum process describing the dynamics of a driven qubit in a structured reservoir. The motivation for this study is twofold: on one hand, we study the differences and analogies of the non-Markovianity measures, and on the other hand, we investigate the effect o...

We consider two recently proposed measures of non-Markovianity applied to a particular quantum process describing the dynamics of a driven qubit in a structured reservoir. The motivation of this study is twofold: on one hand, we study the differences and analogies of the non-Markovianity measures and on the other hand, we investigate the effect of...

A non-Markovian master equation is obtained for a two level atom driven by a phase noisy laser. The derivation is based on obtaining an equation for the density operator of the system averaged over the previous histories of the external noise. Averaging over the current value of the noise variable by means of the Zwanzig–Nakajima projection operato...

We derive a quantum linear Boltzmann equation from first principles to describe collisional friction, diffusion, and decoherence in a unified framework. In doing so, we discover that the previously celebrated quantum contribution to position diffusion is not a true physical process, but rather an artifact of the use of a coarse-grained time scale n...

We derive a quantum master equation from first principles to describe friction in one dimensional, collisional Brownian motion. We are the first to avoid an ill-defined square of the Dirac delta function by using localized wave packets rather than plane waves. Solving the Schr\"odinger equation for two colliding particles, we discover that the prev...

An examination is made of the conditions under which the detection record generated by the quantum trajectory simulation of the output of a detector continuously monitoring an open Markovian system is ergodic, i.e. where the time averages of a single realization of such a record will yield the same result as an ensemble average over many such reali...

We analyze decoherence-free (DF) quantum information in the presence of an arbitrary non-nearest-neighbor bath-induced system Hamiltonian using a Markovian master equation. We show that the most appropriate encoding for N qubits is probably contained within the ~(2/9) N excitation subspace. We give a timescale over which one would expect to apply o...

We develop the work of Christandl [Phys. Rev. A 71, 032312 (2005)], to show how a d -hypercube homogenous network can be dressed by additional links to perfectly route quantum information between any given input and output nodes in a duration that is independent of the routing chosen and, surprisingly, the size of the network.

We analyze the stability of super- and subradiant states in a system of identical two-level atoms in the near-Dicke limit, i.e., when the atoms are very close to each other compared to the wavelength of resonant light. The dynamics of the system are studied using a renormalized master equation, both with multipolar and minimal-coupling interaction...

We study adiabatic population transfer between discrete positions. Being closely related to STIRAP in optical systems, this transport is coherent and robust against variations of experimental parameters. Thanks to these properties the scheme is a promising candidate for transport of quantum information in quantum computing. We study the effects of...

The unequal time commutators of the field operators of the free electromagnetic field, and their physical interpretation in terms of the simultaneous measurability of the EM field components at different space time points, have long been known since the work of Jordan and Pauli, and Bohr and Rosenfeld. The behaviour of these commutators can be unde...

Non-Markovian master equations are constructed from underlying classical stochastic processes. These equations therefore have quantum trajectory unravellings, including unravellings that have an immediate measurement interpretation, usually only found for Markovian (Lindblad) master equations.

We derive a master equation describing the evolution of a quantum system subjected to a sequence of observations. These measurements occur randomly at a given rate and can be of a very general form. As an example, we analyse the effects of these measurements on the evolution of a two-level atom driven by an electromagnetic field. For the associated...

It is shown that complete information on the micromaser cavity field correlation function and hence the spectrum for the cavity field at absolute zero is encoded on the atomic beam exiting from the cavity. A possible means of measuring the atomic beam correlation function is discussed.

We present a quantum theory of friction in which interactions with the surrounding medium are described by generalized measurements of the particle's position and momentum. The theory predicts intrinsically quantum contributions to the particle's steady-state energy and to the associated diffusion in position. We discuss the physical significance o...

We derive a master equation describing the evolution of a quantum system subjected to a sequence of observations. These measurements occur randomly at a given rate and can be of a very general form. As an example, we analyse the effects of these measurements on the evolution of a two-level atom driven by an electromagnetic field. For the associated...

We derive a quantum theory of matter-wave detection from microscopic considerations. We calculate both the short-time approximation and the long-time correction to the detection rate of matter waves. The detection rate can be related to the flux of the matter waves through a detector medium.

We present a Markovian quantum theory of friction. Our approach is based on the idea that collisions between a Brownian particle and single molecules of the surrounding medium constitute, as far as the particle is concerned, instantaneous simultaneous measurements of its position and momentum.

From a microscopic model describing the detection process for matter waves, we derive a quantum theory of matter wave detection. We use perturbation theory to calculate the short-time approximation to the detection rate of matter waves and a Langevin-type calculation to obtain the long-time correction. In both instances we show that the detection r...

We derive a solution for a two-level system evolving adiabatically under the influence of a driving field, which includes open system effects. This solution, which is obtained by working in the representation corresponding to the eigenstates of the time-dependent Hermitian Hamiltonian, enables the dynamic and geometric phases of the evolving densit...

The prevailing description for dissipative quantum dynamics is given by the Lindblad form of a Markovian master equation, used under the assumption that memory effects are negligible. However, in certain physical situations, the master equation is essentially of a non-Markovian nature. In this paper we examine master equations that possess a memory...

We show how the physical processes responsible for the spontaneous decay of a dipole atom conspire to guarantee that the spontaneous decay rate of the atom transforms between different inertial reference frames exactly as required by time dilation. The method employed makes use of familiar basic properties of Maxwell's equations and special relativ...

A Heisenberg equation-of-motion method is developed for deriving the stochastic Schrödinger equations and master equations for non-Markovian open systems. Exact results are obtained for a damped harmonic oscillator, and a damped two level atom, and a perturbative method developed for the driven two level atom.

A method is presented by which the stochastic Schrödinger equation can be derived for systems coupled to a reservoir in cases in which the system-reservoir interaction is non-Markovian, and under the condition that the initial system reservoir state is decorrelated. The method is based on a Heisenberg equation of motion approach applied in conjunct...

The theory of the intensity correlations between photons of different frequencies is re-examined from basic principles and is found to lead to an expression for the correlation function containing operator products which are normally ordered in time. This expression leads to results which are free of certain extra contributions that arise in anothe...

In this paper results are reported for the application of the quantum trajectory method to analysing the dynamics of the micromaser. The master equation for the cavity field is derived by a method which highlights the close relationship between the quantum trajectory method and the usual model for the one-atom micromaser. Possible quantum trajector...

The Mower sequential decay theory of quantum processes has been extended in order formally to remove certain spurious poles in the matrix elements of the resolvent operator, and to recast the results into a more symmetrical general form. A special choice of intermediate manifolds of states leads to a further simplification. An illustrative applicat...

It is shown that the autocorrelation function of the current produced through the ionization of ground-state atoms emerging from a micromaser cavity can be expressed, apart from a shot-noise contribution, in terms of a two-time correlation function of cavity-field variables. Numerical comparisons between this latter correlation function and the int...

We present a nonperturbative result for the spectrum of spontaneous photons emitted by an atom coupled on resonance to a standing-wave cavity mode. Motion of the atom through the standing-wave mode function is included in a classical way. We discuss the form of the spectrum as a function of the velocity of the atom in the limit of strong dipole cou...

A general theory of the micromaser is described. The model is based on treating the input atomic beam as a two-component quantum field so that the two-level atoms in the beam are ‘‘quanta’’ of this field. This approach makes it possible to formulate a general quantum Langevin description of the dynamics with the input atomic field as a source of qu...

The master equation currently used to describe a two level atom interacting with a single mode field damped by contact with a thermal reservoir (the damped Jaynes-Cummings model) is shown not to have, as its steady state solution, the expected canonical density operator prescribed by the general principles of statistical mechanics for a system in t...

Exact solutions in the form of infinite series are well known for the Jaynes-Cummings model describing the interaction of a two-level atom with a single-mode field prepared in a coherent state. While these solutions have led to the discovery of many interesting properties of the Jaynes-Cummings model as a function of time, the nature of the solutio...

In the theoretical study of photoionization, certain properties of the photoelectrons are not defined in terms of any (even idealized) model for the electron-detection process, in contrast to the well-known Glauber theory of photon detection. Thus, for instance, the energy spectrum of the electron produced in atomic ionization is usually defined si...

The Jaynes-Cummings model is one of the most basic systems in quantum optics. It is exactly soluble but the quantities of interest are given by infinite oscillating series which cannot be summed. This leads to problems if one wants to learn about the long-time behavior of the system. On the other hand, the time averages of those quantities can be c...

In this paper we derive an expression for the lifetime of excited atomic states taking account of contributions due to nonresonant two-photon transitions. Explicit integration of the two-photon emission spectrum is not required. The results are applied to the case of the hydrogen atom.

The time-dependent spectrum of the light scattered by a collisionally damped two-level atom weakly excited off resonance by a partially coherent laser field is evaluated. Both the collisional and the laser noise are treated as classical Markovian, Gaussian processes while, in addition, the atom is assumed to experience damping and fluctuations that...

A calculation is presented of the unequal-time electric field commutation relation for an electromagnetic field coupled to a general multilevel atom treated as a nonrelativistic system. Use is made of the multipolar Hamiltonian in its dipole approximate form to describe the atom-field interaction. Contributions to the commutator in addition to the...

The influence of quantum noise on the mean beat frequency 〈〈φ̇〉F〉t of a dithered-ring-laser gyroscope is considered. The corresponding Fokker-Planck equation is discussed and approximate analytical expressions and an exact expression for 〈〈φ̇〉F〉t in terms of infinite-matrix continued fractions are obtained. The two approaches are checked against ea...

Not Available New address: Department of Physics and Astronomy, University of Rochester, Rochester, New York, 14627, U.S.A.

This is the final paper in a series dealing with the spectrum of the beat signal of a ring-laser gyro. The remaining region of operation of the gyro for which an approximate expression for the spectrum has not been obtained, i.e., when the laser rotation rate is close to the edge of the unlocked region, is examined here using an approach of a diffe...

This is the second of three papers dealing with the effects of quantum noise on the operation of a ring-laser gyro. Exact expressions for the spectrum and the mean beat frequency of the beat signal are obtained in terms of infinite continued fractions. The spectrum is found to be always separable into a "coherent" δ-function contribution at zero fr...

The effects of quantum noise on the mean beat frequency and spectrum of laser gyroscopes is discussed, a general formulation of the problem is made from a quantum-noise perspective, and analytical results in various limits are obtained. The characteristic behavior of the beat signal in a conventional ring laser is summarized using a novel method th...

The investigation of atomic resonance fluorescence has always been of special interest as a means for the determination of atomic parameters. In addition, information on the interaction mechanism between atoms and radiation can be obtained. In the standard fluorescence experiment the frequency distribution of the incident photons is larger than the...

Under appropriate conditions, the light intensity transmitted by an interferometer filled with a non-linear medium and irradiated by a resonant or near-resonant driving field exhibits one or many hysteresis cycles, and optical bi- or multi-stability. In this paper, we analyze the response of such systems to sudden changes in the driving field. The...

Spine title: Resolvent operator theory and the A.C. Stark effect. Thesis (Ph. D.)--University of Queensland, 1979. Includes bibliography.