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Showing papers in "Physical Review A in 1997"


Journal ArticleDOI
TL;DR: A general theory of quantum error correction based on encoding states into larger Hilbert spaces subject to known interactions is developed and necessary and sufficient conditions for the perfect recovery of an encoded state after its degradation by an interaction are obtained.
Abstract: Quantum error correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding states into larger Hilbert spaces subject to known interactions. We obtain necessary and sufficient conditions for the perfect recovery of an encoded state after its degradation by an interaction. The conditions depend only on the behavior of the logical states. We use them to give a recovery-operator-independent definition of error-correcting codes. We relate this definition to four others: the existence of a left inverse of the interaction, an explicit representation of the error syndrome using tensor products, perfect recovery of the completely entangled state, and an information theoretic identity. Two notions of fidelity and error for imperfect recovery are introduced, one for pure and the other for entangled states. The latter is more appropriate when using codes in a quantum memory or in applications of quantum teleportation to communication. We show that the error for entangled states is bounded linearly by the error for pure states. A formal definition of independent interactions for qubits is given. This leads to lower bounds on the number of qubits required to correct e errors and a formal proof that the classical bounds on the probability of error of e-error-correcting codes applies to e-error-correcting quantum codes, provided that the interaction is dominated by an identity component.

1,260 citations


Journal ArticleDOI
TL;DR: Previous results about the classical information capacity of a noiseless quantum-mechanical communication channel are extended to situations in which the final signal states are mixed states, that is, to channels with noise.
Abstract: This paper extends previous results about the classical information capacity of a noiseless quantum-mechanical communication channel to situations in which the final signal states are mixed states, that is, to channels with noise.

1,159 citations


Journal ArticleDOI
TL;DR: In this paper, the quantum dynamics of a neutral atom Bose-Einstein condensate in a double-well potential, including many-body hard-sphere interactions, were considered.
Abstract: We consider the quantum dynamics of a neutral atom Bose-Einstein condensate in a double-well potential, including many-body hard-sphere interactions. Using a mean-field factorization we show that the coherent oscillations due to tunneling are suppressed when the number of atoms exceeds a critical value. An exact quantum solution, in a two-mode approximation, shows that the mean-field solution is modulated by a quantum collapse and revival sequence.

864 citations


Journal ArticleDOI
TL;DR: An upper limit is given to the amount of quantum information that can be transmitted reliably down a noisy, decoherent quantum channel and a class of quantum error- correcting codes are presented that allow the information transmitted to attain this limit.
Abstract: An upper limit is given to the amount of quantum information that can be transmitted reliably down a noisy, decoherent quantum channel using the high-probability states of quantum sources. A class of quantum error-correcting codes is presented that allows the information transmitted to attain this limit. The result is a quantum analog of Shannon's bound and code for the noisy classical channel [C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, Chicago, 1948)].

802 citations


Journal ArticleDOI
TL;DR: In this paper, an algorithm for quantum-state estimation based on the maximum-likelihood estimation is proposed, which is shown to be overestimated since they do not guarantee the positive definiteness of the reconstructed density matrix.
Abstract: An algorithm for quantum-state estimation based on the maximum-likelihood estimation is proposed. Existing techniques for state reconstruction based on the inversion of measured data are shown to be overestimated since they do not guarantee the positive definiteness of the reconstructed density matrix.

723 citations


Journal ArticleDOI
TL;DR: In this article, the properties of light beams carrying phase singularities, or optical vortices, were studied both in theory and experiment, and the general rule for angular-momentum density distribution in a combined beam was established.
Abstract: We analyze the properties of light beams carrying phase singularities, or optical vortices. The transformations of topological charge during free-space propagation of a light wave, which is a combination of a Gaussian beam and a multiple charged optical vortex within a Gaussian envelope, are studied both in theory and experiment. We revise the existing knowledge about topological charge conservation, and demonstrate possible scenarios where additional vortices appear or annihilate during free propagation of such a combined beam. Coaxial interference of optical vortices is also analyzed, and the general rule for angular-momentum density distribution in a combined beam is established. We show that, in spite of any variation in the number of vortices in a combined beam, the total angular momentum is constant during the propagation.

491 citations


Journal ArticleDOI
TL;DR: This work shows that all one-sided two-party computations (which allow only one of the two parties to learn the result) are necessarily insecure, and constructs a class of functions that cannot be computed securely in any two-sidedTwo-party computation.
Abstract: It had been widely claimed that quantum mechanics can protect private information during public decision in, for example, the so-called two-party secure computation. If this were the case, quantum smart-cards, storing confidential information accessible only to a proper reader, could prevent fake teller machines from learning the PIN (personal identification number) from the customers' input. Although such optimism has been challenged by the recent surprising discovery of the insecurity of the so-called quantum bit commitment, the security of quantum two-party computation itself remains unaddressed. Here I answer this question directly by showing that all one-sided two-party computations (which allow only one of the two parties to learn the result) are necessarily insecure. As corollaries to my results, quantum one-way oblivious password identification and the so-called quantum one-out-of-two oblivious transfer are impossible. I also construct a class of functions that cannot be computed securely in any two-sided two-party computation. Nevertheless, quantum cryptography remains useful in key distribution and can still provide partial security in ``quantum money'' proposed by Wiesner.

448 citations


Journal ArticleDOI
TL;DR: In this article, a model is presented to describe spontaneous type-II parametric downconversion pumped by a broadband source, which differs from the familiar cw-pumped down-conversion in that a broader range of pump energies is available for downconverting.
Abstract: A model is presented to describe spontaneous type-II parametric down-conversion pumped by a broadband source. This process differs from the familiar cw-pumped down-conversion in that a broader range of pump energies is available for down-conversion. The properties of the nonlinear crystal determine how these energies are distributed into the down-converted photons. Because the two photons are polarized along different crystal axes, they have different spectral characteristics and are no longer exactly anticorrelated. As the pump bandwidth is increased, this effect becomes more pronounced. A fourth-order interference experiment is proposed, illustrating some of the features of broadband pumped down-conversion.

438 citations


Journal ArticleDOI
TL;DR: In this paper, a quantum system composed of a cavity field interacting with a movable mirror can be used to generate a large variety of nonclassical states of both the cavity field and the mirror.
Abstract: We describe how a quantum system composed of a cavity field interacting with a movable mirror can be utilized to generate a large variety of nonclassical states of both the cavity field and the mirror. First we consider state preparation of the cavity field. The system dynamics will prepare a single mode of the cavity field in a multicomponent Schr\"odinger-cat state, in a similar manner to that in a Kerr medium. In addition, when two or more cavity modes interact with the mirror, they can be prepared in an entangled state, which may be regarded as a multimode generalization of the even and odd coherent states. We show also that near-number states of a single mode may be prepared by performing a measurement of the position of the mirror. Second we consider state preparation of the mirror and show that this macroscopic object may be placed in a Schr\"odinger-cat-like state by a quadrature measurement of the light field. In addition, we examine the effect of the damping of the motion of the mirror on the field states inside the cavity and compare this with the effect of cavity field damping.

434 citations


Journal ArticleDOI
TL;DR: It is shown that both bounds can be attained simultaneously by an optimal eavesdropping probe, and an upper bound to the accessible information in one basis, for a given error rate in the conjugate basis is derived.
Abstract: We consider the Bennett-Brassard cryptographic scheme, which uses two conjugate quantum bases. An eavesdropper who attempts to obtain information on qubits sent in one of the bases causes a disturbance to qubits sent in the other basis. We derive an upper bound to the accessible information in one basis, for a given error rate in the conjugate basis. Independently fixing the error rates in the conjugate bases, we show that both bounds can be attained simultaneously by an optimal eavesdropping probe. The probe interaction and its subsequent measurement are described explicitly. These results are combined to give an expression for the optimal information an eavesdropper can obtain for a given average disturbance when her interaction and measurements are performed signal by signal. Finally, the relation between quantum cryptography and violations of Bell's inequalities is discussed.

401 citations


Journal ArticleDOI
TL;DR: In this paper, the authors point out formal correspondences between thermodynamics and entanglement and show that entropy of entanglements is the unique measure of entropy for pure states.
Abstract: We point out formal correspondences between thermodynamics and entanglement. By applying them to previous work, we show that entropy of entanglement is the unique measure of entanglement for pure states.

Journal ArticleDOI
TL;DR: In this article, it was shown that quantum entanglement can be used as a substitute for communication when the goal is to compute a function whose input data are distributed among remote parties.
Abstract: We show that quantum entanglement can be used as a substitute for communication when the goal is to compute a function whose input data are distributed among remote parties. Specifically, we show that, for a particular function among three parties (each of which possesses part of the function's input), a prior quantum entanglement enables one of them to learn the value of the function with only two bits of communication occurring among the parties, whereas, without quantum entanglement, three bits of communication are necessary. This result contrasts the well-known fact that quantum entanglement cannot be used to simulate communication among remote parties.

Journal ArticleDOI
TL;DR: In this paper, the authors describe the dynamics of a multilevel V-type atomic system (including the case of a two-level system) which interacts with a reservoir modeled by a generalized density of states.
Abstract: Atoms can nowadays be placed in increasingly exotic environments such as microscopic cavities and materials with photonic band gaps. High-Q cavities can now easily result in a strong coupling between an atom and its environment where perturbation theory should no longer be appropriate. The purpose of this paper is to describe the dynamics of a multilevel V-type atomic system (including the case of a two-level system) which interacts with a reservoir modeled by a generalized density of states. A theoretical construct, the pseudomode, is utilized to develop general methods for solution. Without using perturbation theory the equivalent master equation is developed and the relationship between the master equation, the pseudomodes, and the generalized density of states function is explored with examples. Utilizing a straightforward definition of the pseudomode, it is found that many functions for the density of states lead to problematic non-Lindblad master equations. Several examples are given, and it is shown how to convert the non-Lindblad master equations into a Lindblad form in these cases. The examples include a non-Lorentzian resonance and a simple model of a photonic band gap.

Journal ArticleDOI
TL;DR: In this article, two independent Bose-Einstein condensates, each initially containing a well-defined number of atoms, were shown to appear coherent in an experiment that measures the beat note between these condensate.
Abstract: We show that two independent Bose-Einstein condensates, each initially containing a well-defined number of atoms, will appear coherent in an experiment that measures the beat note between these condensates. We investigate the role played by atomic interactions within each condensate in the time evolution of their relative phase.

Journal ArticleDOI
M. Dakna1, T. Anhut1, Tomáš Opatrný1, Ludwig Knöll1, D.-G. Welsch1 
TL;DR: In this paper, a scheme for generating Schrodinger-cat-like states of a single-mode optical field by means of conditional measurement is proposed, where a squeezed vacuum is fed into a beam splitter and counting the photons in one of the output channels, the conditional states in the other output channel exhibit a number of properties similar to those of superpositions of two coherent states with opposite phases.
Abstract: A scheme for generating Schr\"odinger-cat-like states of a single-mode optical field by means of conditional measurement is proposed. Feeding a squeezed vacuum into a beam splitter and counting the photons in one of the output channels, the conditional states in the other output channel exhibit a number of properties that are very similar to those of superpositions of two coherent states with opposite phases. We present analytical and numerical results for the photon-number and quadrature-component distributions of the conditional states and their Wigner and Husimi functions. Further, we discuss the effect of realistic photocounting on the states.

Journal ArticleDOI
TL;DR: In this article, the emission spectra of the transition metals Cr, Mn, Fe, Co, Ni, and Cu were measured, employing a single-crystal diffractometer optimized for minimal instrumental broadening.
Abstract: The $K{\ensuremath{\alpha}}_{1,2}$ and $K{\ensuremath{\beta}}_{1,3}$ emission spectra of the $3d$ transition metals Cr, Mn, Fe, Co, Ni, and Cu were measured, employing a single-crystal diffractometer optimized for minimal instrumental broadening. The high-accuracy diffractometer, and the interferometrically calibrated silicon crystal employed ensure absolute wavelengths in the metric scale to a sub-part-per-million accuracy. An accurate analytic representation of each line, obtained by a fit to a minimal set of Lorentzians, is presented. The absolute energies, linewidths, and indices of asymmetry, derived from the data, agree well with previous measurements. So do also the intensity ratios $K{\ensuremath{\alpha}}_{2}/K{\ensuremath{\alpha}}_{1}$ and $K{\ensuremath{\beta}}_{1,3}/K{\ensuremath{\alpha}}_{1,2},$ which are, however, slightly, but consistently, higher than previous values. Possible origins for the observed $Z$-dependent trends are discussed.

Journal ArticleDOI
TL;DR: In this article, a variational technique is applied to solve the time-dependent nonlinear Schrodinger equation, with the goal to model the dynamics of dilute ultracold atom clouds in the Bose-Einstein condensed phase.
Abstract: A variational technique is applied to solve the time-dependent nonlinear Schrodinger equation ~Gross- Pitaevskii equation! with the goal to model the dynamics of dilute ultracold atom clouds in the Bose-Einstein condensed phase We derive analytical predictions for the collapse, equilibrium widths, and evolution laws of the condensate parameters and find them to be in very good agreement with our numerical simulations of the nonlinear Schrodinger equation It is found that not only the number of particles, but also both the initial width of the condensate and the effect of different perturbations to the condensate may play a crucial role in the collapse dynamics The results are applicable when the shape of the condensate is sufficiently simple @S1050-2947~97!04408-9# PACS number~s!: 0375Fi

Journal ArticleDOI
TL;DR: A family of quantum codes for the QEC, the quantum Bose-Chaudhuri-Hocquenghem codes, that can be efficiently decoded is introduced.
Abstract: The quantum erasure channel (QEC) is considered. Codes for the QEC have to correct for erasures, i.e., arbitrary errors at known positions. We show that four quantum bits are necessary and sufficient to encode one quantum bit and correct one erasure, in contrast to five quantum bits for unknown positions. Moreover, a family of quantum codes for the QEC, the quantum Bose-Chaudhuri-Hocquenghem codes, that can be efficiently decoded is introduced.

Journal ArticleDOI
TL;DR: In this paper, the authors present a numerical study of second-harmonic (SH) generation in a one-dimensional, generic, photonic band-gap material that is doped with a nonlinear medium.
Abstract: We present a numerical study of second-harmonic (SH) generation in a one-dimensional, generic, photonic band-gap material that is doped with a nonlinear ${\ensuremath{\chi}}^{(2)}$ medium. We show that a 20-period, 12-\ensuremath{\mu}m structure can generate short SH pulses (similar in duration to pump pulses) whose energy and power levels may be 2--3 orders of magnitude larger than the energy and power levels produced by an equivalent length of a phase-matched, bulk medium. This phenomenon comes about as a result of the combination of high electromagnetic mode density of states, low group velocity, and spatial phase locking of the fields near the photonic band edge. The structure is designed so that the pump pulse is tuned near the first-order photonic band edge, and the SH signal is generated near the band edge of the second-order gap. This maximizes the density of available field modes for both the pump and SH field. Our results show that the ${\ensuremath{\chi}}^{(2)}$ response is effectively enhanced by several orders of magnitude. Therefore, mm- or cm-long, quasi-phase-matched devices could be replaced by these simple layered structures of only a few micrometers in length. This has important applications to high-energy lasers, Raman-type sources, and frequency up- and down-conversion schemes.

Journal ArticleDOI
TL;DR: In this paper, an approach to describe the phase matching of high harmonics emitted by laser driven atoms in a nonperturbative regime, for which the atomic response displays an intrinsic intensity-dependent phase was presented.
Abstract: We present an approach to describe the phase matching of high harmonics emitted by laser driven atoms in a nonperturbative regime, for which the atomic response displays an intrinsic intensity-dependent phase. We show that the traditional phase-matching conditions involving conservation of wave vectors should be modified by taking into account the gradient of this atomic phase. We investigate various focusing geometries and interpret the numerical results of Sali`eres et al. [Phys. Rev. Lett. 74, 3776 (1995)]. Within the framework of the two-step model, we demonstrate that the gradient of the intensity-dependent phase can be considered as the canonical momentum gained by the electron in the continuum due to acceleration by field-gradient forces, including in particular the ponderomotive force.

Journal ArticleDOI
TL;DR: In this paper, the authors calculate the heating rates arising from laser intensity noise and beam-pointing fluctuations in far-off resonance optical traps, and show that intensity noise causes exponential heating, while beampointing noise causes heating at a constant rate.
Abstract: Using a simple model, we calculate the heating rates arising from laser intensity noise and beam-pointing fluctuations in far-off resonance optical traps. Intensity noise causes exponential heating, while beam-pointing noise causes heating at a constant rate. The achievement of heating time constants well beyond 10 sec imposes stringent requirements on the laser noise power spectra. Noise spectra are measured for a commercial argon-ion laser to illustrate the expected time scales.

Journal ArticleDOI
TL;DR: In this paper, the spontaneous parametric down-conversion (SPDC) of a continuous wave pump is studied for the case of a pulse, where the pump pulse acts like a clock with an uncertainty equal to its width.
Abstract: Spontaneous parametric down-conversion (SPDC) has been extensively studied for the case of a continuous wave pump. In this paper SPDC is studied for the case in which the pump is a pulse. The pump pulse acts like a clock with an uncertainty equal to its width. This makes it possible to distinguish pairs of photons born at sufficiently different depths inside the crystal with a consequent decrease in two-photon interference. We study this effect in detail for degenerate collinear type-II SPDC and degenerate type-I SPDC. It may be possible in the type-II case to eliminate the clock effect of the pump by judicious choice of materials and wavelengths.

Journal ArticleDOI
TL;DR: In this article, it was shown that a Schrodinger cat state can be generated in a resonator with an oscillating wall, and the effects due to the environmental couplings with this nonlinear system were considered by developing an operator perturbation procedure to solve the master equation for the field mode density operator.
Abstract: It is shown that because of the radiation pressure a Schr\"odinger cat state can be generated in a resonator with an oscillating wall. The optomechanical control of quantum macroscopic coherence and its detection is taken into account by introducing new cat states. The effects due to the environmental couplings with this nonlinear system are considered by developing an operator perturbation procedure to solve the master equation for the field mode density operator.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the orbital angular momentum per photon is doubled, which conserves the angular angular momentum in the light beam, and that the frequency-doubled output beam has a Gegenbauer-Gaussian amplitude distribution at the beam waist.
Abstract: Laguerre-Gaussian modes of various order are frequency doubled. The azimuthal phase structure of the second-harmonic light is measured directly by interfering the beam with its mirror image. We show that the orbital angular momentum per photon is doubled, so conserving the orbital angular momentum in the light beam. The frequency-doubled output beam is shown to have a Gegenbauer-Gaussian amplitude distribution at the beam waist. The beam can be described as a summation of Laguerre-Gaussian modes that interfere so that it changes form with propagation, but the distribution at the beam waist is reproduced in the far field.

Journal ArticleDOI
TL;DR: In this paper, a simple analytical solution for the problem of multiphoton detachment from negative ions by a linearly polarized laser field is found, which is valid in a wide range of intensities and frequencies of the field, from the perturbation theory to the tunneling regime, and is applicable to the excess-photon as well as near-threshold detachment.
Abstract: A simple analytical solution for the problem of multiphoton detachment from negative ions by a linearly polarized laser field is found. It is valid in the wide range of intensities and frequencies of the field, from the perturbation theory to the tunneling regime, and is applicable to the excess-photon as well as near-threshold detachment. Practically, the formulas are valid when the number of photons is greater than one. They produce the total detachment rates, relative intensities of the excess-photon peaks, and photoelectron angular distributions for the hydrogen and halogen negative ions, in agreement with those obtained in other, more numerically involved calculations in both perturbative and nonperturbative regimes. Our approach explains the extreme sensitivity of the multiphoton detachment probability to the asymptotic behavior of the bound-state wave function. Rapid oscillations in the angular dependence of the n-photon detachment probability are shown to arise due to interference of the two classical trajectories, which lead to the same final state after the electron emerges at diametrically opposite sides of the atom when the field is close to maximal.

Journal ArticleDOI
TL;DR: In this paper, the ionization dynamics of small rare-gas clusters in intense, ultrafast laser fields are studied via classical trajectory Monte Carlo simulations, and it is shown that for similar laser pulses the charge states reached by atoms in a cluster can be significantly higher than those for atoms in the gas phase.
Abstract: The ionization dynamics of small rare-gas clusters in intense, ultrafast laser fields are studied via classical trajectory Monte Carlo simulations. Our results indicate that for similar laser pulses the charge states reached by atoms in a cluster can be significantly higher than those for atoms in the gas phase. The ionization enhancement is strongly dependent on the cluster density and exhibits a rapid increase in charge state once the laser intensity has reached the threshold for single ionization. This {open_quotes}ionization ignition model{close_quotes} is driven by the combination of the laser field and the strong field from the ionized cluster atoms. Approximate atomic inner-shell ionization probabilities are calculated for several cluster densities and peak laser intensities and provide evidence for the generation of inner-shell holes on an ultrafast time scale. This is a necessary condition for the generation of x-ray pulses with temporal widths comparable to that of the driving laser pulses. {copyright} {ital 1997} {ital The American Physical Society}

Journal ArticleDOI
TL;DR: In this article, it was shown that one is by no means constrained to entangled spin systems, and to Stern-Gerlach apparatuses, and the concept of generalized Bell numbers was employed, which is more suitable than the standard set of spin eigenvalues.
Abstract: Multiport beam splitters are shown to be applicable in feasible optical realizations of higher-dimensional EPR correlations, and of tests of local realism involving measurements of nondichotomic variables. These multiports permit optical realizations of any unitary operator in Hilbert spaces of arbitrary finite dimension. Thus it is shown that one is by no means constrained to entangled spin systems, and to Stern-Gerlach apparatuses. In the analysis the concept of generalized Bell numbers is employed, which is more suitable than the standard set of spin eigenvalues. The results presented here move the discussion on entangled higher-than- spin systems from the realm of gedanken experiments to real experiments.

Journal ArticleDOI
TL;DR: In this article, the authors generalized the Bogoliubov method for the excitation spectrum of a Bose-condensed gas to apply to a gas with an exact large number $N$ of particles.
Abstract: The Bogoliubov method for the excitation spectrum of a Bose-condensed gas is generalized to apply to a gas with an exact large number $N$ of particles. This generalization yields a description of the Schr\"odinger picture field operators as the product of an annihilation operator $A$ for the total number of particles and the sum of a ``condensate wave function'' $\ensuremath{\xi}(\mathbf{x})$ and a phonon field operator $\ensuremath{\chi}(\mathbf{x})$ in the form $\ensuremath{\psi}(\mathbf{x})\ensuremath{\approx}A{\ensuremath{\xi}(\mathbf{x})+\ensuremath{\chi}(\mathbf{x})/\sqrt{N}}$ when the field operator acts on the $N$ particle subspace. It is then possible to expand the Hamiltonian in decreasing powers of $\sqrt{N}$, and thus obtain solutions for eigenvalues and eigenstates as an asymptotic expansion of the same kind. It is also possible to compute all matrix elements of field operators between states of different $N$. The excitation spectrum can be obtained by essentially the same method as Bogoliubov only if $\ensuremath{\xi}(\mathbf{x})$ is a solution of the time-independent Gross-Pitaevskii equation for $N$ particles and any chemical potential $\ensuremath{\mu}$, which yields a valid and stable solution of the Gross-Pitaevskii equation. The treatment within a subspace of fixed $N$ is identical in form to that usually used, but the interpretation of the operators is slightly different. A time-dependent generalization is then made, yielding an asymptotic expansion in decreasing powers of $\sqrt{N}$ for the equations of motion. In this expansion the condensate wave function has the time-dependent form $\ensuremath{\xi}(\mathbf{x},t)$, and the condition for the validity of the expansion is that $\ensuremath{\xi}(\mathbf{x},t)$ satisfies the time-dependent Gross-Pitaevskii equation $\ensuremath{\partial}\ensuremath{\xi}/\ensuremath{\partial}t=\ensuremath{-}({\ensuremath{\Elzxh}}^{2}/2m){\ensuremath{ abla}}^{2}\ensuremath{\xi}+V\ensuremath{\xi}+Nu|\ensuremath{\xi}{|}^{2}\ensuremath{\xi}$. The physics is then described in a kind of interaction picture, called the condensate picture, in which the phonon operator can be expressed as $\ensuremath{\chi}(\mathbf{x},t)={\ensuremath{\sum}}_{k}{\ensuremath{\xi}}_{k}(\mathbf{x},t){\ensuremath{\alpha}}_{k},$ where the operators ${\ensuremath{\alpha}}_{k}$ are time-independent annihilation operators, and the state vector has a time evolution described by a Schr\"odinger equation in which the Hamiltonian is a time-dependent quadratic form in the phonon creation and annihilation operators, whose coefficients are explicitly determined in terms of the time-dependent condensate wave function $\ensuremath{\xi}(\mathbf{x},t)$.

Journal ArticleDOI
TL;DR: In this article, the authors point out the connection of these ''breathing'' modes to the presence of a hidden symmetry, i.e., the two-dimensional Lorentz group, allowing pulsating solutions to be constructed for the interacting quantum system and for the corresponding nonlinear Gross Pitaevskii equation.
Abstract: Atoms confined in a harmonic potential show universal oscillations in two dimensions (2D). We point out the connection of these ``breathing'' modes to the presence of a hidden symmetry. The underlying symmetry SO(2,1), i.e., the two-dimensional Lorentz group, allows pulsating solutions to be constructed for the interacting quantum system and for the corresponding nonlinear Gross-Pitaevskii equation. We point out how this symmetry can be used as a probe for recently proposed experiments of trapped atoms in 2D.

Journal ArticleDOI
TL;DR: In this paper, a quantum-classical mixing is studied by a group-theoretical approach, and a quantumclassical equation of motion is derived, which preserves the Lie algebra structure of quantum and classical mechanics.
Abstract: Quantum-classical mixing is studied by a group-theoretical approach, and a quantum-classical equation of motion is derived. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics, and, therefore, leads to a natural description of interaction between quantum and classical degrees of freedom. The exact formalism is applied to coupled quantum and classical oscillators. Various approximations, such as the mean-field and the multiconfiguration mean-field approaches, which are of great utility in studying realistic multidimensional systems, are derived. Based on the formulation, a natural classification of the previously suggested quantum-classical equations of motion arises, and several problems from earlier works are resolved.