We consider two identical, mutually delay-coupled semiconductor lasers and show that their compound laser modes (CLMs)—the basic continuous wave solutions—depend rather sensitively on the pump current of the lasers. Specifically, we show with figures and accompanying animations how the underlying CLM structure and the associated locking region, where both lasers operate stably with the same frequency, change as a function of the pump current. Our results provide a natural transition between rather different CLM structures that have been reported in the literature. Moreover, we demonstrate how the locking region as well as the different types of instabilities at its boundary depend on the pump current. This is of fundamental interest for the dynamics of coupled lasers and their possible application.
Many-particle confinement (localization) is studied for a 1D system of spinless fermions with nearest-neighbor hopping and interaction, or equivalently, for an anisotropic Heisenberg spin-1/2 chain. This system is frequently used to model quantum computers with perpetually coupled qubits. We construct a bounded sequence of site energies that leads to strong single-particle confinement of all states on individual sites. We show that this sequence also leads to a confinement of all many-particle states in an infinite system for a time that scales as a high power of the reciprocal hopping integral. The confinement is achieved for strong interaction between the particles while keeping the overall bandwidth of site energies comparatively small. The results show viability of quantum computing with time-independent qubit coupling.
Linear-optical passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the algebraic structure of LOP transformations and quantum computing. We first show how to decompose the Fock space of N optical modes in finite-dimensional subspaces that are suitable for encoding strings of qubits and invariant under LOP transformations (these subspaces are related to the spaces of irreducible unitary representations of U(N). Next we show how to design in algorithmic fashion LOP circuits which implement any quantum circuit deterministically. We also present some simple examples, such as the circuits implementing a cNOT gate and a Bell state generator/analyser.
Two, non-interacting two-level atoms immersed in a common bath can become mutually entangled when evolving with a Markovian, completely positive dynamics. For an environment made of external quantum fields, this phenomenon can be studied in detail: one finds that entanglement production can be controlled by varying the bath temperature and the distance between the atoms. Remarkably, in certain circumstances, the quantum correlations can persist in the asymptotic long-time regime.
We address the spatial shape of entangled photon states generated in spontaneous parametric downconversion in non-collinear geometries, when the interacting waves exhibit Poynting vector walk-off. We discuss how such shape depends on the interplay between the state ellipticity caused by the non-collinear geometry, and the Poynting vector walk-off. In particular, we study the impact of the new features exhibited by walking entangled photons on the implementation of quantum protocols based on the spiral spectra of the entangled photons.
This topical issue of Journal of Optics B: Quantum and Semiclassical Optics contains 16 contributions devoted to quantum systems with moving boundaries. In a broad sense, the papers continue the studies opened exactly 100 years ago by Einstein in his seminal work on the electrodynamics of moving bodies and the quantum nature of light. Another jubilee which we wish to celebrate by launching this issue is the 80th anniversary of the publication of two papers, where the first solutions of the classical Maxwell equations in a one-dimensional cavity with moving boundaries were obtained, by T H Havelock (1924 Some dynamical illustrations of the pressure of radiation and of adiabatic invariance Phil. Mag. 47 754–71) and by E L Nicolai (1925 On a dynamical illustration of the pressure of radiation Phil. Mag. 49 171–7). As was shown by Einstein, studying the fluctuations of the electromagnetic field inevitably leads one to its quantum (corpuscular) nature. Many papers in this issue deal with problems where moving boundaries produce parametric excitation of vacuum fluctuations of the field, which could result in several different observable effects, like the modification of the famous Casimir force, or the creation of real quanta from the vacuum. It is worth emphasizing that these phenomena, frequently referred to as nonstationary (or dynamical) Casimir effects, are no longer the province only of pure theorists: some experimental groups have already started long-term work aimed at observing such effects in the laboratory. Of course, many difficult problems remain to be resolved before this dream becomes reality. Several papers here show both important progress in this direction, and possible difficulties still to be tackled. Problems that have been considered include, in particular, decoherence, entanglement, and the roles of geometry and polarization. Other papers deal with fundamental problems like the Unruh effect, the interaction of accelerated relativistic atoms with radiation, vacuum friction, and so on. Solutions of some interesting problems of nonrelativistic quantum mechanics with time-dependent boundary conditions, including applications to Bose–Einstein condensates, can also be found here. Since nonstationary Casimir effects can exist not only for photons but for any other quanta (e.g., phonons in solids or in liquid helium), we believe the approaches and results presented in this collection will find interesting applications in other branches of physics too. One possible example might be the generation of squeezed and other 'nonclassical' states of different fields by time-dependent boundary conditions. Approximately half the contributed papers stem from talks at two recent conferences: the First International Workshop on Problems with Moving Boundaries, organized by Professor J Dittrich in Prague in October 2003, and the International Workshop on the Dynamical Casimir Effect, organized by Professor G Carugno in Padua in June 2004. We wish to thank all the authors and reviewers for their efforts in preparing high quality papers, which we hope will attract the attention of other researchers, and especially of young people, to the fascinating areas covered by this special issue.
Using the approach to quantum entanglement based on the quantum fluctuations of observables, we show the existence of perfect entangled states of a single 'spin-1' particle. We give physical examples related to photons and condensed matter physics.
A time-dependent dielectric cmedium is used to model a time-varying beam-splitter inside a cavity. The time-varying boundary conditions smoothly evolve from a highly transmitting to a highly reflecting beam-splitter. These approximately correspond to a transformation from a single cavity to a pair of cavities. Quantum field-theoretic calculations show that such a smooth change yields non-singular evolution of the field. However, it predicts a production of photons up to frequencies comparable to the rate of change of the transition. We find that a time-varying beam-splitter operating at optical frequencies would produce an observable number of photons.
We study the creation of photons in resonant cylindrical cavities with time-dependent length. The physical degrees of freedom of the electromagnetic field are described using Hertz potentials. We describe the general formalism for cavities with arbitrary section. Then we compute explicitly the number of TE and TM motion-induced photons for cylindrical cavities with rectangular and circular sections. We also discuss the creation of TEM photons in non-simply connected cylindrical cavities.
We study the decoherence of even and odd superpositions of displaced number states in the frameworks of the standard master equation, describing phase insensitive attenuators and amplifiers. We compare different possible definitions of the 'decoherence time' and show that the frequently used approaches based on the time derivatives of some quantities (such as the 'quantum purity'), taken at the initial moment, are not quite satisfactory for quantum states characterized by several parameters, due to the absence of the scaling laws. Defining the conditional decoherence time as the time necessary for diminishing the interference peak of the Wigner function to the given relative level, we study its dependence on the initial distance between peaks |α|, excitation number m and parameters of the reservoir. We show that highly excited states with can be more robust against decoherence than the coherent superpositions with m = 0.
We show that squeezed spin states achieved through nonlinear interactions are eigenstates of a non-Hermitian operator, which however enjoys the property of pseudo-Hermiticity such that the resulting eigenvalues are real. We represent the squeezed states in terms of Wigner d-matrices, making the evaluation of squeezing straightforward. We show that the spin squeezing can go up to 70%.
Controlling the dynamics or measurement of quantum systems via the manipulation of external parameters is a most important phenomenon that lies at the heart of several fields including atomic and optical physics, molecular chemistry and quantum information. As quantum technologies have matured, a host of practical applications of quantum control have been realized in quantum optics, cavity QED, atomic spin ensembles, ion trapping, and Bose--Einstein condensation. As a result, quantum control theory is a rapidly growing research field.
Non-local properties of symmetric two-qubit states are quantified in terms of a complete set of entanglement invariants. We prove that negative values of some of the invariants are signatures of quantum entanglement. This leads us to identify sufficient conditions for non-separability in terms of entanglement invariants. Non-local properties of two-qubit states extracted from (i) the Dicke state, (ii) a state generated by a one-axis twisting Hamiltonian, and (iii) a one-dimensional Ising chain with nearest neighbour interaction are analysed in terms of the invariants characterizing them.
We consider the degrees of controllability of multi-partite quantum systems, as well as necessary and sufficient criteria for each case. The results are applied to the problem of simultaneous control of an ensemble of quantum dots with a single laser pulse. Finally, we apply optimal control techniques to demonstrate selective excitation of individual dots for a simultaneously controllable ensemble of quantum dots.
We consider a consistent model of a quantum damped harmonic oscillator with arbitrary time-dependent frequency and damping coefficients in the frameworks of the Heisenberg-Langevin equations with two noncommuting delta-correlated noise operators. For the 'minimal noise' set of correlation functions, which have the same time dependence as the damping coefficient, we obtain the exact solution, which is the generalization of Husimi's solution for the undamped nonstationary oscillator. The model is applied to the problem of the photon creation from vacuum or thermal states due to the nonstationary Casimir effect inside the cavity with periodical time-dependent conductivity of the thin semiconductor boundary layer, simulating the periodical displacements of the wall. The general formula for the rate of photon generation under the resonance conditions in the presence of dissipation is obtained.
Photon counting induces an effective non-linear optical phase shift in certain states derived by linear optics from single photons. Although this non-linearity is non-deterministic, it is sufficient in principle to allow scalable linear optics quantum computation (LOQC). The most obvious way to encode a qubit optically is as a superposition of the vacuum and a single photon in one mode-so-called 'single-rail' logic. Until now this approach was thought to be prohibitively expensive (in resources) compared to 'dual-rail' logic where a qubit is stored by a photon across two modes. Here we attack this problem with real-time feedback control, which can realize a quantum-limited phase measurement on a single mode, as has been recently demonstrated experimentally. We show that with this added measurement resource, the resource requirements for single-rail LOQC are not substantially different from those of dual-rail LOQC. In particular, with adaptive phase measurements an arbitrary qubit state a alpha/0 > + beta/1 > can be prepared deterministically.
We derive the interaction Hamiltonian of a Laguerre-Gaussian beam with a simple atomic system, under the assumption of a small spread of the center of mass wave function in comparison with the waist of the Laguerre-Gaussian beam. The center of mass motion of the atomic system is taken into account. Using the properties of regular spherical harmonics the internal and center of mass coordinates are separated without making any multipolar expansion. Then the selection rules of the internal and of the center of mass motion transitions follow immediately. The influence of the winding number of the Laguerre-Gaussian beams on the selection rules and transition probability of the center of mass motion is discussed.
Multiphoton detachment rates for the H− 1S ground state irradiated by a weak trichromatic ac field consisting of the fundamental frequency ω = 0.272 eV and its second, third or fourth higher harmonics were computed from first principles. The weak intensities are in the range of 107–108 W cm−2. The calculations incorporated systematically electronic structure and electron correlation effects. They were done by implementing a time-independent, nonperturbative many-electron, many-photon theory (MEMPT) which obtains cycle-averaged complex eigenvalues, whose real part gives the field-induced energy shift, Δ, and the imaginary part is the multiphoton ionization rate, Γ. Through analysis, plausible arguments and computation, we show that when the intensities are weak the dependence of Γ on phase differences is simple. Specifically, Γs are depicted in the form of plane surfaces, with minor ripples due to higher order ionization paths, in terms of trigonometric functions of the phase differences. This dependence is likely to be applicable to other atomic systems as well, and to provide a definition of the weak field regime in the trichromatic case. When the field intensities are such that higher order ionization paths become important, these dependences break down and we reach the strong field regime.
We investigate the influence of atomic interactions on the tunnelling of sodium condensates across a spatially oscillating optical barrier. In the limit of very fast barrier oscillations, in which resonant tunnelling via a metastable state takes place, the interactions affect the position and lineshape of the transmission peak. We anticipate that the possibility of modulating the interactions in a tunnelling condensate can be exploited to achieve nonlinear effects such as optical limiting and bistability.
The short time dynamics of a quantum Brownian particle in a harmonic potential is studied in the phase space. An exact non-Markovian analytic approach to calculate the time evolution of the Wigner function is presented. The dynamics of the Wigner function of an initially squeezed state is analyzed. It is shown that virtual exchanges of energy between the particle and the reservoir, characterizing the non-Lindblad short time dynamics where system-reservoir correlations are not negligible, show up in the phase space.
