Showing papers in "Physical Review A in 1995"
TL;DR: U(2) gates are derived, which derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number of unitary operations on arbitrarily many bits.
Abstract: We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values (x,y) to (x,x ⊕y)) is universal in the sense that all unitary operations on arbitrarily many bits n (U(2 n )) can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical AND of all remaining input bits is satisfied. These gates play a central role in many proposed constructions of quantum computational networks. We derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number required for arbitrary n-bit unitary operations.
3,731 citations
TL;DR: In the mid-1990s, theorists devised methods to preserve the integrity of quantum bits\char22{}techniques that may become the key to practical quantum computing on a large scale.
Abstract: In the mid-1990s, theorists devised methods to preserve the integrity of quantum bits---techniques that may become the key to practical quantum computing on a large scale.
3,668 citations
TL;DR: In this article, a two-photon optical imaging experiment was performed based on the quantum nature of the signal and idler photon pairs produced in spontaneous parametric down-conversion, where an aperture placed in front of a fixed detector is illuminated by the signal beam through a convex lens.
Abstract: A two-photon optical imaging experiment was performed based on the quantum nature of the signal and idler photon pairs produced in spontaneous parametric down-conversion. An aperture placed in front of a fixed detector is illuminated by the signal beam through a convex lens. A sharp magnified image of the aperture is found in the coincidence counting rate when a mobile detector is scanned in the transverse plane of the idler beam at a specific distance in relation to the lens.
1,651 citations
IBM1
TL;DR: A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit.
Abstract: A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The best previous result had shown the universality of three-bit gates, by analogy to the universality of the Toffoli three-bit gate of classical reversible computing. Two-bit quantum gates may be implemented by magnetic resonance operations applied to a pair of electronic or nuclear spins. A ``gearbox quantum computer'' proposed here, based on the principles of atomic-force microscopy, would permit the operation of such two-bit gates in a physical system with very long phase-breaking (i.e., quantum-phase-coherence) times. Simpler versions of the gearbox computer could be used to do experiments on Einstein-Podolsky-Rosen states and related entangled quantum states.
1,073 citations
TL;DR: A simple, fully analytic method of calculating the amount of radiation emitted by optical solitons perturbed by higher-order dispersion effects in fibers is demonstrated and finds good agreement with numerical results.
Abstract: We demonstrate a simple, fully analytic method of calculating the amount of radiation emitted by optical solitons perturbed by higher-order dispersion effects in fibers and find good agreement with numerical results. It is pointed out that this radiation mechanism is analogous to the well-known Cherenkov radiation processes in nonlinear optics. © 1995 The American Physical Society.
775 citations
TL;DR: In this article, a nonrelativistic Hamiltonian of the interaction between a moving mirror and radiation pressure was derived directly from the equation of motion of a moving moving mirror, and the wave equation with timevarying boundary conditions.
Abstract: We present a nonrelativistic Hamiltonian of the interaction between a moving mirror and radiation pressure. This Hamiltonian is derived directly from the equation of motion of a moving mirror, and the wave equation with time-varying boundary conditions. We discuss the canonical quantization of both the field and the motion of the mirror.
572 citations
TL;DR: The ionization rate of the H{sub 2}{sup +} molecular ion in intense, short-pulse laser fields is found to exhibit maxima at large {ital R}, exceeding the atom limit by an order of magnitude.
Abstract: We study the ionization of the ${\mathrm{H}}_{2}^{+}$ molecular ion in intense, short-pulse laser fields by numerically solving the three-dimensional time-dependent Schr\"odinger equation as a function of internuclear distance $R$. Anomalously high ionization for the molecular ion at large internuclear separations is observed for orientations parallel to the linearly polarized laser field. The ionization rate is found to exhibit maxima at large $R$, exceeding the atom limit by an order of magnitude. This is attributed to transitions between pairs of chargeresonant states which are strongly coupled by the field in diatomic molecular ions. The effect is shown to also occur in higher odd-charge diatomic molecular ions and can be attributed to field-induced nonadiabatic transitions between the charge-resonant states and electron tunneling suppression by the instantaneous Stark field of the laser.
570 citations
TL;DR: The role of phase anisotropy in the laser cavity is explored close to threshold and it is predicted that it stabilizes two preferred orthogonal directions of polarization, which, however, are discriminated in their stability properties by transverse effects.
Abstract: A four-level model which takes account of the polarization of the laser field by including the spin sublevels of the conduction and valence bands of a semiconductor allows us to introduce vector rate equations which account for the polarization degree of freedom of the laser emission. Analysis of these rate equations and their extension to include transverse degrees of freedom provides important physical insight into the nature of polarization instabilities in surface-emitting semiconductor lasers. In the absence of transverse effects the model predicts a marginally stable linearly polarized state. The type of dynamical response of the polarization degrees of freedom is linked to the relative time scale of spontaneous-emission and spin-relaxation processes. With transverse effects included, we predict the existence of stable transverse spatially homogeneous intensity outputs with arbitrary direction of linear polarization in the transverse plane. The stability of the off-axis emission solutions to long-wavelength perturbations is investigated and, in addition to an Eckhaus instability associated with a global phase, we predict a polarization instability associated with a relative phase of the complex field vector. The role of phase anisotropy in the laser cavity is explored close to threshold and we predict that it stabilizes two preferred orthogonal directions of polarization, which, however, are discriminated in their stability properties by transverse effects.
565 citations
TL;DR: A theory of electromagnetically induced transparency in a three-level, ladder-type Doppler-broadened medium is developed, paying special attention to the case where the coupling and probe beams are counterpropagating and have similar frequencies, so as to reduce the total Dopplers width of the two-photon process.
Abstract: We develop a theory of electromagnetically induced transparency in a three-level, ladder-type Doppler-broadened medium, paying special attention to the case where the coupling and probe beams are counterpropagating and have similar frequencies, so as to reduce the total Doppler width of the two-photon process. The theory is easily generalized to deal with the \ensuremath{\Lambda} configuration, where the ideal arrangement involves two copropagating beams. We discuss different possible regimes, depending on the relative importance of the various broadening mechanisms, and identify ways to optimize the absorption-reduction effect. The theory is compared to the results of a recent experiment (on a ladder-type system), using the Rb D2 line, with generally very good agreement. The maximum absorption reduction observed (64.4%) appears to be mostly limited by the relatively large (\ensuremath{\sim}5 MHz) linewidth of the diode lasers used in our experiment.
563 citations
TL;DR: The treatment of adiabatic perturbations within density-functional theory is examined, at arbitrary order of the perturbation expansion, and the general expressions are specialized for the second, third, and fourth derivative of the energy.
Abstract: The treatment of adiabatic perturbations within density-functional theory is examined, at arbitrary order of the perturbation expansion. Due to the extremal property of the energy functional, standard variation-perturbation theorems can be used. The different methods (Sternheimer equation, extremal principle, Green's function, and sum over state) for obtaining the perturbation expansion of the wave functions are presented. The invariance of the Hilbert space of occupied wave functions with respect to a unitary transformation leads to the definition of a ''parallel-transport-gauge'' and a ''diagonal-gauge'' perturbation expansion. Then, the general expressions are specialized for the second, third, and fourth derivative of the energy, with an example of application of the method up to third order.
512 citations
TL;DR: It is found that for quantum calculations (in which the maintenance of coherence over a large number of states is important), not only must the coupling be small, but the time taken in the quantum calculation must be less than the thermal time scale.
Abstract: The effects of the inevitable coupling to external degrees of freedom of a quantum computer are examined. It is found that for quantum calculations (in which the maintenance of coherence over a large number of states is important), not only must the coupling be small, but the time taken in the quantum calculation must be less than the thermal time scale \ensuremath{\Elzxh}/${\mathit{k}}_{\mathit{B}}$T. For longer times the condition on the strength of the coupling to the external world becomes much more stringent.
TL;DR: This work discusses quantum cryptographic protocols based on the transmission of weak coherent states and presents a system, based on a symbiosis of two existing systems, for which the information available to the eavesdropper is significantly reduced and is therefore safer than the two previous ones.
Abstract: The safety of a quantum key distribution system relies on the fact that any eavesdropping attempt on the quantum channel creates errors in the transmission. For a given error rate, the amount of information that may have leaked to the eavesdropper depends on both the particular system and the eavesdropping strategy. In this work, we discuss quantum cryptographic protocols based on the transmission of weak coherent states and present a system, based on a symbiosis of two existing systems, for which the information available to the eavesdropper is significantly reduced. This system is therefore safer than the two previous ones. We also suggest a possible experimental implementation.
TL;DR: In this article, the authors presented numerical results from solving the time-dependent nonlinear Schrodinger equation that describes an inhomogeneous, weakly interacting Bose-Einstein condensate in a small harmonic trap potential at zero temperature.
Abstract: We present numerical results from solving the time-dependent nonlinear Schr\"odinger equation (NLSE) that describes an inhomogeneous, weakly interacting Bose-Einstein condensate in a small harmonic trap potential at zero temperature. With this method we are able to find solutions for the NLSE for ground state condensate wave functions in one dimension or in three dimensions with spherical symmetry. These solutions corroborate previous ground state results obtained from the solution of the time-independent NLSE. Furthrmore, we can examine the time evolution of the macroscopic wave function even when the trap potential is changed on a time scale comparable to that of the condensate dynamics, a situation that can be easily achieved in magneto-optical traps. We show that there are stable solutions for atomic species with both positive and negative s-wave scattering lengths in one-dimensional (1D) and 3D systems for a fixed number of atoms. In both the 1D and 3D cases, these negative scattering length solutions have solitonlike properties. In 3D, however, these solutions are only stable for a modest range of nonlinearities. We analyze the prospects for diagnosing Bose-Einstein condensation in a trap using several experiments that exploit the time-dependent behavior of the condensate.
TL;DR: The phase of the induced atomic dipole moment exhibits a piecewise-linear dependence on the laser intensity, and is related to the action acquired by the electron during its motion in the laser held.
Abstract: A recently formulated theory of high-order harmonic generation by low-frequency laser fields [Anne L'Huillier et al., Phys. Rev. A 48, R3433 (1993)] allows us to study the phase of the induced atomic dipole moment. We show that this phase exhibits a piecewise-linear dependence on the laser intensity. This dependence can be interpreted in quasiclassical terms, and is related to the action acquired by the electron during its motion in the laser held. The value of the phase, however, is also affected by the quantum effects of tunneling, diffusion, and interference. The phase of the dipole moment considerably influences the conversion efficiency, as well as the coherence properties, of the harmonics generated in macroscopic media.
TL;DR: An implementation of a quantum computer to solve Deutsch's problem, which requires exponential time on a classical computer but only linear time with quantum parallelism, is proposed by using a dual-rail quantum-bit representation as a simple form of error correction.
Abstract: We propose an implementation of a quantum computer to solve Deutsch's problem, which requires exponential time on a classical computer but only linear time with quantum parallelism. By using a dual-rail quantum-bit representation as a simple form of error correction, our machine can tolerate some amount of decoherence and still give the correct result with high probability. The design that we employ also demonstrates a signature for quantum parallelism which unambiguously distinguishes the desired quantum behavior from the merely classical. The experimental demonstration of our proposal using quantum optical components calls for the development of several key technologies common to single photonics.
TL;DR: This paper analyzes the controllability of quantum systems arising in molecular dynamics as systems with finite numbers of levels, and examines their controllable status.
Abstract: In this paper we analyze the controllability of quantum systems arising in molecular dynamics. We model these systems as systems with finite numbers of levels, and examine their controllability. To do this we pass to their unitary generators and use results on the controllability of invariant systems on Lie groups. Examples of molecular systems, modeled as finite-dimensional control systems, are provided. A simple algorithm to detect the controllability of a molecular system is provided. Finally, we apply this algorithm to a five-level system.
TL;DR: The alternative theory helps to explain the surprising accuracy of LSD and GGA energies, and suggests that the correct solution of the Kohn-Sham equations in LSD or GGA is the fully self-consistent broken-symmetry single determinant of lowest total energy.
Abstract: In the standard interpretation of spin-density functional theory, a self-consistent Kohn-Sham calculation within the local spin density (LSD) or generalized gradient approximation (GGA) leads to a prediction of the total energy E, total electron density n(r)=${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$(r)+${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$(r), and spin magnetization density m(r)=${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$(r)-${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$(r). This interpretation encounters a serious ``symmetry dilemma'' for ${\mathrm{H}}_{2}$, ${\mathrm{Cr}}_{2}$, and many other molecules. Without changing LSD or GGA calculational methods and results, we escape this dilemma through an alternative interpretation in which the third physical prediction is not m(r) but the on-top electron pair density P(r,r), a quantity more directly related to the total energy in the absence of an external magnetic field. This alternative interpretation is also relevant to antiferromagnetic solids. We argue that the nonlocal exchange-correlation energy functional, which must be approximated, is most nearly local in the alternative spin-density functional theory presented here, less so in the standard theory, and far less so in total-density functional theory. Thus, in LSD or GGA, predictions of spin magnetization densities and moments are not so robust as predictions of total density and energy. The alternative theory helps to explain the surprising accuracy of LSD and GGA energies, and suggests that the correct solution of the Kohn-Sham equations in LSD or GGA is the fully self-consistent broken-symmetry single determinant of lowest total energy.
TL;DR: In this article, the vibronic motion of a trapped ion far from the Lamb-Dicke regime can be described by a strongly nonlinear, multiquantum Jaynes-Cummings model.
Abstract: We show that the vibronic motion of a trapped ion far from the Lamb-Dicke regime can be described, under appropriate resonance conditions, by a strongly nonlinear, multiquantum Jaynes-Cummings model. In contrast to previous nonlinear or multiphoton generalizations of the Jaynes-Cummings model, it could presently be realized in experiments.
TL;DR: In this paper, an iterative predictor-corrector finite-difference time-domain method is used to solve the semiclassical Maxwell-Bloch system numerically without invoking any of the standard approximations such as the rotating-wave approximation.
Abstract: An iterative predictor-corrector finite-difference time-domain method is used to solve the semiclassical Maxwell-Bloch system numerically without invoking any of the standard approximations such as the rotating-wave approximation. This approach permits a more exact study of self-induced transparency effects in a two-level atom. In addition to recovering the standard results, for instance, for \ensuremath{\pi}, 2\ensuremath{\pi}, and 4\ensuremath{\pi} pulses, several features in the results appear at the zeros of the driving pulse, where its time derivatives are maximum. Several ultrafast-pulse examples demonstrate that time-derivative-driven nonlinearities have a significant impact on the time evolution of a two-level atom system. Moreover, typical small-signal gain results are also obtained with our Maxwell-Bloch simulator. We illustrate that these time-derivative effects can be used to design an ultrafast, single-cycle pump pulse that completely inverts the two-level atom population. A pump-probe signal set is then used to illustrate gain in the probe signal.
TL;DR: High-order frequency mixing experiments using the radiation of a high-power Ti:sapphire laser and its second harmonic are described and discussed and a three-dimensional quantum-mechanical calculation with a delta-function potential has been applied, showing quite good agreement with the experiments.
Abstract: High-order frequency mixing experiments using the radiation of a high-power Ti:sapphire laser and its second harmonic are described and discussed. Linearly and circularly polarized light fields with comparable intensities have been used. For the theoretical description a three-dimensional quantum-mechanical calculation with a \ensuremath{\delta}-function potential has been applied, showing quite good agreement with the experiments.
TL;DR: A general demonstration of the existence of variational principles for an even order of perturbation, when constraints are present, is provided here.
Abstract: When perturbation theory is applied to a quantity for which a variational principle holds (eigenenergies of Hamiltonians, Hartree-Fock or density-functional-theory energy, etc.), different variational perturbation theorems can be derived. A general demonstration of the existence of variational principles for an even order of perturbation, when constraints are present, is provided here. Explicit formulas for these variational principles for even orders of perturbation, as well as for the ''2n + 1 theorem,'' to any order of perturbation, with or without constraints, are also exhibited. This approach is applied to the case of eigenenergies of quantum-mechanical Hamiltonians, studied previously by other methods.
TL;DR: In this article, the authors present an empirical model for the cesium magneto-optical trap, with particular regard to the best combination of atomic density and temperature that can be produced, and show that both the nonlinear variation with position of the restoring force and the reabsorption of photons scattered in the cloud limit the maximum density.
Abstract: We present an investigation of the cesium magneto-optical trap, with particular regard to the best combination of atomic density and temperature that can be produced. Conditions in the trap depend on four independent parameters: the detuning and intensity of the light, the gradient of the magnetic field, and the number of atoms trapped. We have varied all these parameters and measured the temperature and density distribution of the trapped cloud. Both the nonlinear variation with position of the restoring force and the reabsorption of photons scattered in the cloud limit the maximum density, and we present an empirical model that takes this into account. This in turn limits the density in phase space \ensuremath{\rho} (defined as the number of atoms in a box with sides of one thermal de Broglie wavelength). We have observed a maximum \ensuremath{\rho}=(1.5\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$, with a spatial density of about 2\ifmmode\times\else\texttimes\fi{}${10}^{11}$ atoms/${\mathrm{cm}}^{3}$.
TL;DR: Generally, good agreement with experiment is obtained with the available differential, integrated, ionization, and total cross sections, as well as with the electron-impact coherence parameters up to and including the 3 {sup 3}{ital D}-state excitation.
Abstract: We present the convergent close-coupling theory for the calculation of electron-helium scattering. We demonstrate its applicability at a range of projectile energies of 1.5 to 500 eV to scattering from the ground state to n\ensuremath{\le}3 states. Generally, good agreement with experiment is obtained with the available differential, integrated, ionization, and total cross sections, as well as with the electron-impact coherence parameters up to and including the 3 $^{3}$D-state excitation. This agreement is shown to be overall the best of the currently used electron-helium scattering theories. On occasion, some significant discrepancies with experiment are observed, particularly for the triplet-state excitations.
TL;DR: The observation of planar dark spatial solitons due to the bulk photovoltaic effect in lithium niobate, with intensities of the order of 10 W/cm2 and widths of approximately 20 μm, is reported.
Abstract: We report on the observation of planar dark spatial solitons due to the bulk photovoltaic effect in lithium niobate, with intensities of the order of 10 W/cm2 and widths of approximately 20 \ensuremath{\mu}m. Photovoltaic solitons display a characteristic tensorial dependence on their direction of propagation, on their polarization, and on the orientation of the amplitude profile, with respect to the principal axes of the crystalline medium. The index perturbation associated with a dark soliton persists in the dark, and it can trap and guide a second beam.
TL;DR: It is shown that the time profile of the harmonics emitted by a single atom exposed to a strong electromagnetic field may be obtained through a wavelet or a Gabor analysis of the acceleration of the atomic dipole, shedding some light on the competition between the atomic excitation or ionization processes and photon emission.
Abstract: We show that the time profile of the harmonics emitted by a single atom exposed to a strong electromagnetic field may be obtained through a wavelet or a Gabor analysis of the acceleration of the atomic dipole. This analysis is extremely sensitive to the details of the dynamics and sheds some light on the competition between the atomic excitation or ionization processes and photon emission. For illustration we study the interaction of atomic hydrogen with an intense laser pulse.
TL;DR: Instantaneous Galilean invariance is used to derive from first principles the expression for the Hamiltonian of an electron with a position-dependent effective mass, as well as the adequate boundary conditions for the wave function in the case of abrupt heterojunctions.
Abstract: Instantaneous Galilean invariance is used to derive from first principles the expression for the Hamiltonian of an electron with a position-dependent effective mass, as well as the adequate boundary conditions for the wave function in the case of abrupt heterojunctions. A very elementary model sustaining these results in the envelope-function approximation is also proposed.
TL;DR: The Talbot effect, the self-imaging of a periodic structure, with atom waves is demonstrated, and the successive recurrence of these self-images is measured as a function of the distance from the imaged grating.
Abstract: We have demonstrated the Talbot effect, the self-imaging of a periodic structure, with atom waves. We have measured the successive recurrence of these self-images as a function of the distance from the imaged grating. This is a near-field interference effect, which has several possible applications that are discussed.
TL;DR: In this paper, the resonance properties of ultracold ground state collisions were investigated and the locations of various resonances and their corresponding error bounds due to the uncertainty of the interatomic potentials were presented.
Abstract: We investigate the resonance properties of ultracold ground state $^{6}\mathrm{Li}$${+}^{6}$Li, $^{7}\mathrm{Li}$${+}^{7}$Li, and $^{23}\mathrm{Na}$${+}^{23}$Na collisions. The locations of various resonances and their corresponding error bounds due to the uncertainty of the interatomic potentials are presented. Also, the resonance widths are computed using rigorous coupled-channel calculations, as well as a modified version of Feshbach theory valid for strong fields.