Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

The properties of a unique set of quantum states of the electromagnetic field are reviewed. These ‘squeezed states’ have less uncertainty in one quadrature than a coherent state. Proposed schemes for the generation and detection of squeezed states as well as potential applications are discussed.

Squeezed states of light

We show that under the influence of pure vacuum noise two entangled qubits become completely disentangled in a finite-time, and in a specific example we find the time to be given by ln((2+sqrt[2] / 2) times the usual spontaneous lifetime.

https://arxiv.org/pdf/quant-ph/0404161.pdf

Finite-time disentanglement via spontaneous emission.

We construct a general measure for the degree of non-Markovian behavior in open quantum systems. This measure is based on the trace distance which quantifies the distinguishability of quantum states. It represents a functional of the dynamical map describing the time evolution of physical states, and can be interpreted in terms of the information flow between the open system and its environment. The measure takes on nonzero values whenever there is a flow of information from the environment back to the open system, which is the key feature of non-Markovian dynamics.

Measure for the degree of non-markovian behavior of quantum processes in open systems.

The Jaynes-Cummings model (JCM), a soluble fully quantum mechanical model of an atom in a field, was first used (in 1963) to examine the classical aspects of spontaneous emission and to reveal the existence of Rabi oscillations in atomic excitation probabilities for fields with sharply defined energy (or photon number). For fields having a statistical distributions of photon numbers the oscillations collapse to an expected steady value. In 1980 it was discovered that with appropriate initial conditions (e.g. a near-classical field), the Rabi oscillations would eventually revive, only to collapse and revive repeatedly in a complicated pattern. The existence of these revivals, present in the analytic solutions of the JCM, provided direct evidence for discreteness of field excitation (photons) and hence for the truly quantum nature of radiation. Subsequent study revealed further non-classical properties of the JCM field, such as a tendency of the photons to antibunch. Within the last two years it ha...

The Jaynes-Cummings Model

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" $\ensuremath{\delta}$-function contribution at zero frequency, representing the effects of locking, and an "incoherent" part of nonzero band-width. Computed forms for the spectrum and the frequency response curve are presented for parameter values appropriate to the ring-laser gyro. The results obtained show that for laser rotation rates corresponding to the locked zone in the absence of noise, the tendency for locking as measured by the strength of the coherent contribution continues to dominate, but this effect rapidly becomes negligibly small outside this zone. In addition, the transition in beat frequency between the locked and unlocked zones which is discontinuous in the noise-free case ceases to be well defined in the presence of noise. Finally, the higher harmonics predicted to occur in the unlocked zone in the absence of noise are found to reoccur in the presence of noise except that the individual harmonics are now found to be broadened.

Quantum noise in ring-laser gyros. II. Numerical results

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 strong, this model may become invalid. We derive a master equation for two coupled harmonic oscillators that are subject to individual heat baths modeled by a collection of harmonic oscillators and show that this master equation in general contains nonlocal Lindblad terms. We compare the resulting time evolution with that obtained for dissipation through local Lindblad terms for each individual oscillator and show that the evolution is different in the two cases. In particular, the two descriptions give different predictions for the steady state and for the entanglement between strongly coupled oscillators. This shows that when describing strongly coupled harmonic oscillators, one must take great care in how dissipation is modeled and that a description using local Lindblad terms may fail. This may be particularly relevant when attempting to generate entangled states of strongly coupled quantum systems.

/pdf/markovian-evolution-of-strongly-coupled-harmonic-oscillators-48wi9gtd6n.pdf

Markovian evolution of strongly coupled harmonic oscillators

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 quantum noise. The passage to a master-equation description is then effected by use of an adjoint-operator method, and by introducing a general class of statistical states for the atomic beam known as generalized shot noise

Quantum-field model of the injected atomic beam in the micromaser.

For any master equation which is local in time, whether Markovian, non-Markovian, of Lindblad form or not, a general procedure is reviewed for constructing the corresponding linear map from the initial state to the state at time t, including its Kraus-type representations. Formally, this is equivalent to solving the master equation. For an N-dimensional Hilbert space it requires (i) solving a first order N^2 x N^2 matrix time evolution (to obtain the completely positive map), and (ii) diagonalising a related N^2 x N^2 matrix (to obtain a Kraus-type representation). Conversely, for a given time-dependent linear map, a necessary and sufficient condition is given for the existence of a corresponding master equation, where the (not necessarily unique) form of this equation is explicitly determined. It is shown that a `best possible' master equation may always be defined, for approximating the evolution in the case that no exact master equation exists. Examples involving qubits are given.

/pdf/finding-the-kraus-decomposition-from-a-master-equation-and-315t3zj8zb.pdf

Finding the Kraus decomposition from a master equation and vice versa

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 another version of this theory which contains non-normally ordered products. The analysis presented is based on a description of the frequency-filtering process in terms of Fabry-Perot interferometers. The mirrors of the interferometers are modelled as classical dielectrics. The EM field in the presence of these dielectrics is then quantised and the intensity correlation function defined in terms of these modified field operators. The results are examined in detail for the case of a light field radiated by a two-level atom.

James D. Cresser

Papers

Quantum noise in ring-laser gyros. II. Numerical results

Markovian evolution of strongly coupled harmonic oscillators

Quantum-field model of the injected atomic beam in the micromaser.

Finding the Kraus decomposition from a master equation and vice versa

Intensity correlations of frequency-filtered light fields