Showing papers on "Quantum state published in 1990"
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TL;DR: The quantum Zero effect is the inhibition of transitions between quantum states by frequent measurements of the state by means of pulses of light in an rf transition between two ground-state hyperfine levels.
Abstract: The quantum Zero effect is the inhibition of transitions between quantum states by frequent measurements of the state. The inhibition arises because the measurement causes a collapse (reduction) of the wave function. If the time between measurements is short enough, the wave function usually collapses back to the initial state. We have observed this effect in an rf transition between two $^{9}$${\mathrm{Be}}^{+}$ ground-state hyperfine levels. The ions were confined in a Penning trap and laser cooled. Short pulses of light, applied at the same time as the rf field, made the measurements. If an ion was in one state, it scattered a few photons; if it was in the other, it scattered no photons. In the latter case the wave-function collapse was due to a null measurement. Good agreement was found with calculations.
977 citations
TL;DR: It is shown that the integral of the uncertainty of energy with respect to time is independent of the particular Hamiltonian used to transport the quantum system along a given curve in the projective Hilbert space, which gives a new time-energy uncertainty principle.
Abstract: For an arbitrary quantum evolution, it is shown that the integral of the uncertainty of energy with respect to time is independent of the particular Hamiltonian used to transport the quantum system along a given curve in the projective Hilbert space. It is the distance along this curve measured by the Fubini-Study metric. This gives a new time-energy uncertainty principle. New geometric meanings to time as measured by a clock and the transition probability during a quantum measurement are also obtained.
680 citations
TL;DR: It is proposed by which the quantum states of two light beams of different frequencies can be interchanged and it is possible to generate frequency-tunable squeezed light for spectroscopic applications.
Abstract: An experimental scheme is proposed by which the quantum states of two light beams of different frequencies can be interchanged. With this scheme it is possible to generate frequency-tunable squeezed light for spectroscopic applications.
342 citations
TL;DR: In this paper, the equivalence of the partial cross-sections calculated using these time-dependent quantum-mechanical methods to those calculated using standard time-independent quantum theory is explicitly demonstrated.
Abstract: The time-dependent quantum-mechanical description of molecular photodissociation processes is briefly reviewed. A new easily implementable method for the calculation of partial cross-sections to produce specific fragment quantum states is presented. The equivalence of the partial cross-sections calculated using these time-dependent quantum-mechanical methods to those calculated using standard time-independent quantum theory is explicitly demonstrated. Sample calculations using a model potential-energy surface for a system having physical parameters corresponding to the H2S molecule are presented. The power of the method is clearly demonstrated by explicitly showing, for this model system, how a single time-dependent calculation yields the partial photodissociation cross-sections for all photon energies. We furthermore point out the suitability of modern parallel computing techniques in connection with such methods.
310 citations
TL;DR: In this article, the structure of the tensor product representation of the quantum groupSLq(2,C) was investigated by using the 2-dimensional quantum plane as a building block.
Abstract: We investigate the structure of the tensor product representation of the quantum groupSLq(2,C) by using the 2-dimensional quantum plane as a building block. Two types of 4-dimensional spaces are constructed applying the methods used in twistor theory. We show that the 4-dimensional real representation ofSLq(2,C) generates a consistent non-commutative algebra, and thus it provides a quantum deformation of Minkowski space. The transformation of this 4-dimensional space gives the quantum Lorentz groupSOq(3, 1).
181 citations
TL;DR: A review of different mathematical formalizations of the physical concept "two observables (or two systems) are independent" that have been proposed in quantum theories, particularly relativistic quantum field theory, can be found in this paper.
Abstract: A review is made of the multitude of different mathematical formalizations of the physical concept ‘two observables (or two systems) are independent’ that have been proposed in quantum theories, particularly relativistic quantum field theory. The most basic mathematical formulation of independence in any quantum theory is what one may call kinematical independence: the two observables, resp. the observables of the two quantum systems, which are represented by elements of a C*-algebra, resp. two subalgebras of a C*-algebra, are required to commute. This is related to a mathematical formulation of the notion of the coexistence (or compatibility) of two observables. Another basic notion of independence, generally called statistical independence in the literature, is, roughly speaking, two quantum systems are said to be statistically independent if each can be prepared in any state, how ever the other system has been prepared. There are numerous mathematical formulations of this notion and their interrelationships are explained. Statistical independence and kinematical independence are shown to be logically independent. Additional notions such as strict locality and their relation to statistical independence are discussed. The mathematics of a more quantitative measure of statistical independence, Bell’s inequalities, is reviewed and its relations with previously introduced notions are indicated. All of these notions are then viewed in application to relativistic quantum field theory.
167 citations
TL;DR: In this paper, the authors solved the Fateev-Zamolodchikov quantum spin chain (i.e., the spin-1 XXZ quantum Heisenberg chain) with a class of boundary terms by the quantum inverse scattering method.
141 citations
TL;DR: In this article, the authors considered the quantisation of the two-dimensional toric and spherical phase spaces in analytic coherent state representations, and showed that the distribution of the zeros in the phase space becomes one-dimensional for integrable systems, and highly spread out (conceivably uniform) for chaotic systems.
Abstract: The quantisation of the two-dimensional toric and spherical phase spaces is considered in analytic coherent state representations. Every pure quantum state admits therein a finite multiplicative parametrisation by the zeros of its Husimi function. For eigenstates of quantised systems, this description explicitly reflects the nature of the underlying classical dynamics: in the semiclassical regime, the distribution of the zeros in the phase space becomes one-dimensional for integrable systems, and highly spread out (conceivably uniform) for chaotic systems. This multiplicative representation thereby acquires a special relevance for semiclassical analysis in chaotic systems.
138 citations
TL;DR: This work describes a method for generating superpositions of classically distinguishable quantum states in an optical-frequency mode using the optical back-action-evading apparatus demonstrated recently by La Porta, Slusher, and Yurke.
Abstract: We describe a method for generating superpositions of classically distinguishable quantum states in an optical-frequency mode. The method uses the optical back-action-evading apparatus demonstrated recently by La Porta, Slusher, and Yurke [Phys. Rev. Lett. 62, 28 (1989)].
108 citations
TL;DR: By presqueezing the signal port input, it is found that gain requirements of the back-action evader are much less demanding and the asymptotic behavior of the output is determined.
Abstract: We analyze a quantum nondemolition measurement scheme similar to that advocated by Song, Caves, and Yurke [Phys. Rev. A 41, 5261 (1990)] for generating superpositions of macroscopically distinct quantum states, but with the parametric amplifier and the back-action evader interchanged. We determine the asymptotic behavior of the output and obtain the conditions under which a superposition of two coherent states is approached. By presqueezing the signal port input, we find that gain requirements of the back-action evader are much less demanding.
100 citations
TL;DR: In this article, the authors find the states of light which have minimum phase variance both for a given maximum energy state component and a given mean energy component, and when these states contain sufficiently many photon number state components, the number state coefficients approximate sinusoidal and Airy functions respectively.
TL;DR: In this article, the lowest ten vibrational excited state energies of H2O and H2CO in the Born-Oppenheimer approximation were calculated using correlation function quantum Monte Carlo.
Abstract: Using a new Monte Carlo method for computing properties of excited quantum states, correlation function quantum Monte Carlo, we calculate the lowest ten vibrational excited state energies of H2O and H2CO in the Born–Oppenheimer approximation. The statistical errors for H2O are 0.1 cm−1 for the ground state and 15 cm−1 for the tenth excited state while for H2CO they are 2 cm−1 for the ground state and 30 cm−1 for the eighth excited state. The algorithm presented here is easily extensible to larger systems.
TL;DR: The proposed formalism reduces to known equations in the Markovian case and two recent models for spontaneous quantum state reduction have been recovered in the framework of the theory.
Abstract: We have proposed a formal theory for the continuous measurement of relativistic quantum fields We have also derived the corresponding scattering equations The proposed formalism reduces to known equations in the Markovian case Two recent models for spontaneous quantum state reduction have been recovered in the framework of our theory A possible example of the relativistic continuous measurement has been outlined in standard quantum electrodynamics The continuous measurement theory possesses an alternative formulation in terms of interacting quantum and stochastic fields
TL;DR: In this paper, an abstract definition of a quantum mechanical switch is given that allows for the continual random fluctuations in the warm wet environment of the brain, among several switch-like entities in the brain.
Abstract: A human brain operates as a pattern of switching. An abstract definition of a quantum mechanical switch is given that allows for the continual random fluctuations in the warm wet environment of the brain. Among several switch-like entities in the brain, I choose to focus on the sodium channel proteins. After explaining what these are, I analyse the ways in which my definition of a quantum switch can be satisfied by portions of such proteins. I calculate the perturbing effects of normal variations in temperature and electric field on the quantum state of such a portion. These are shown to be acceptable within the fluctuations allowed for by my definition. Information processing and unpredictability in the brain are discussed. The ultimate goal underlying the paper is an analysis of quantum measurement theory based on an abstract definition of the physical manifestations of consciousness. The paper is written for physicists with no prior knowlecge of neurophysiology, but enough introductory material has also been included to allow neurophysiologists with no prior knowledge of quantum mechanics to follow the central arguments.
TL;DR: The quantum group symmetry is realized in the Coulomb gas version of the C < 1 models in this article, where the representation spaces of the quantum group are defined in terms of screened vertex operators and the number of screening operators is interpreted as the genuine quantum group number.
TL;DR: In this article, a quantum theory for continuous photodetection processes that describes nonunitary time development of the field under continuous measurement of photon number is developed. But the quantum theory is restricted to the case where the photon number does not change.
Abstract: We develop a quantum theory for continuous photodetection processes that describes nonunitary time development of the field under continuous measurement of photon number. Exact expressions are obtained for time evolutions of the photon-field density operator, average and variance of the photon number, and the Fano factor. These are applied to typical quantum states, i.e., number, coherent, thermal, and squeezed states. The continuous photodetection process is made up of two elementary processes in terms of the referring measurement process, that is, one-count and no-count processes. Just after the one-count process in which a photodetector registers one photoelectron, the average photon number 〈n(t)〉 of the remaining field is shown to increase for super-Poissonian states (e.g., thermal state) and decrease for sub-Poissonian states (e.g., number state); for the Poissonian state (e.g., coherent light), 〈n(t)〉 does not change. During the no-count process in which the photodetector registers no photoelectrons, on the other hand, 〈n(t)〉 decreases in time for all states except the number state. The physical origins for these results are clarified from the viewpoint of nonunitary state reduction by continuous measurement of photon number. Furthermore, we introduce a nonreferring measurement process in which the detector registers photocounts, but we discard all readout information. We discuss the difference in the way the photon field evolves in this process compared to the referring measurement process.
TL;DR: Employing electrostatic confinement with a dual-gate device, periodic arrays of electron dots on Si widely tunable in diameter and electron number are realized, indicating a direct effect of strong quantum confinement.
Abstract: Employing electrostatic confinement with a dual-gate device we realize periodic arrays of electron dots on Si widely tunable in diameter and electron number. From far-infrared transmission studies of dimensional resonances, we deduce dot diameters down to 40 nm for as little as 20 electrons in quantum states spaced by more than 5 meV. Excitation energies as well as mode dispersions in finite magnetic fields are found to strongly depend on the strength and the shape of the lateral confining potential. A detailed analysis of the oscillator strengths indicates a direct effect of strong quantum confinement.
TL;DR: In this article, a simple generating function was used to calculate the entropy of random quantum states for finite-dimensional Hilbert spaces over real, complex and quaternionic scalars, and the authors extended their previous formula for the quantum correlation information of a state determination apparatus to include real and Quaternionic von Neumann analyzers.
Abstract: The authors use a simple generating function to calculate exactly the entropy of random quantum states for finite-dimensional Hilbert spaces over real, complex and quaternionic scalars. This allows them to extend their previous formula for the quantum correlation information of a state determination apparatus to include real and quaternionic von Neumann analysers.
01 Jan 1990
TL;DR: In this paper, an approach to quantum groups based on the quantization of Poisson-Lie groups is presented, and the quantum Yang-Baxter Equation and the algebraic definition of quantum groups appear quite naturally.
Abstract: This mini-course presents an approach to quantum groups based on the quantization of Poisson-Lie groups. In this connection the Quantum Yang-Baxter Equation and the algebraic definition of quantum groups appear quite naturally. We discuss quantum groups corresponding to simple Lie groups of classical type, their quantum vector spaces and quantum universal enveloping algebras. In particular the latter are introduced as dual objects to quantum groups with the duality given by a quantum R-matrix.
TL;DR: The superconductivity and superfluid flow in liquid helium are macroscopic quantum phenomena as mentioned in this paper, and they depend on the fact that the energy states of even microscopic objects, although closely spaced, are discrete, and on the statistical mechanics of systems made up of identical particles.
Abstract: As first suggested by Fritz London, superconductivity and superfluid flow in liquid helium are macroscopic quantum phenomena. They depend on the fact that the energy states of even macroscopic objects, although closely spaced, are discrete, and on the statistical mechanics of systems made up of identical particles. The electrons in a superconducting metal, with a spin of one‐half, obey Fermi‐Dirac statistics and the exclusion principle. Helium atoms of isotopic mass 4 obey Einstein‐Bose statistics, in which there can be many particles in the same quantum state, as is the case with photons, the quanta of radiation, if they are regarded as particles.
TL;DR: The quantization of the classical spinning particle with Zitterbewegung leads besides the Dirac electron to a family of generalized Duffin-Kemmer-Petiau particles which are thus all different possible quantum states of the same classical system as mentioned in this paper.
01 Jan 1990
TL;DR: The conceptually simplest interpretation of the quantum-mechanical wave function is that adopted by most textbooks as discussed by the authors, which is the one adopted by Dirac1 and Messiah2.
Abstract: The conceptually simplest interpretation of the quantum-mechanical wave function is that adopted by most textbooks In the celebrated book by Dirac1 one reads — each state of a dynamical system at a particular time corresponds to a ket vector if the ket vector corresponding to a state is multiplied by any complex number, not zero, the resulting ket vector will correspond to the same state (pages 16, 17) And later — a measurement always causes the system to jump into an eigenstate of the dynamical variable that is being measured (page 36) Similar sentences can be found, e g, in the book by Messiah2 (pages 249 and 251) In the above statements the term state refers to a single system, not to a statistical ensemble of systems This emerges clearly from the second statement, concerning reduction, which is quite incomprehensible in this form if the ket vector is not referred to a single system In most textbooks the wave function up to a factor is interpreted just in this way — as the state of the single considered system
TL;DR: In this paper, the authors studied the structure of chaos in the phase space of planar benzene, especially around the local CH stretching mode, and found that the region of phase space within a hyperradius of order h 1/2 (which is the region corresponding to a quantum state) about the local mode is fairly well decoupled from the rest of the phase spaces and changes sharply from highly structured and quasiregular (although unstable) local mode character to chaotic normal mode character away from the CH bond.
Abstract: This article addresses the importance of the structure of chaos in the phase space of planar benzene, especially around the local CH stretching mode. The structure imposes severe constraints on the ability of the classical mechanics to simulate the quantum mechanical flow of the energy out of the local mode, i.e., to simulate intramolecular vibrational relaxation (IVR). The phase space structure is inferred by computing ensemble averaged classical correlation functions and spectral densities. It is found that the region of phase space within a hyperradius of order h1/2 (which is the region corresponding to a quantum state) about the local mode is fairly well decoupled from the rest of the phase space and changes sharply from highly structured and quasiregular (although unstable) local mode character to chaotic normal mode character away from the CH bond. On one hand, the experimentally prepared quantum (packet) system must behave smoothly within the scale of h seeing only the dominant local mode character...
TL;DR: In this article, an analysis of the geometrical phase factor arising in the cyclic evolution of a non-Hermitian Hamiltonian is undertaken, and the validity of the adiabatic approximation is discussed in view of the measurability of this new effect.
Abstract: In a previous paper, the measurement of an atomic Berry phase associated with two crossing levels has been suggested as a possible test for an atomic interferometry method. As one of the two levels involved is radiative, an analysis of geometrical phase factor arising in the cyclic evolution of a non-Hermitian Hamiltonian is undertaken here. It is shown that the use of the dual basis allows a simple generalization of Berry's results and that, in addition to the two possible values encountered in the Hermitian case (0, π), the geometrical phase can take on as intermediate value π/2 or even a complex value, whereas the corresponding quantum states may be permuted. The validity of the adiabatic approximation is discussed in view of the measurability of this new effect.
TL;DR: In this article, two degrees of freedom quantum mechanical calculations on the bound states of H+3 photodissociation spectrum are presented, and the effect of rotational excitation is analyzed.
Abstract: Two degrees of freedom quantum mechanical calculations on the bound states of H+3 are presented. Two different potential energy surfaces are employed. The effect of rotational excitation is analyzed. For J=0, the high energy region is composed largely of states that cannot be assigned. However, two regularly spaced series are observed, corresponding to ‘‘horseshoe’’ states predicted previously by classical calculations. In addition we find a new assignable series of inverted hyperspherical states. Conversely, for high orbiting angular momentum (l=20) in which the proton rotates about the diatom, assignable normal mode states persist up to dissociation. Semiclassical periodic orbit quantization is found to give excellent agreement for the regular quantum states. The significance of these results for the interpretation of the H+3 photodissociation spectrum is discussed.
TL;DR: In this paper, the authors take the label space as the quantum phase space, which plays the same role played by phase space in classical mechanics, some differences coming inevitably from its nonlinear character.
Abstract: The space of labels characterizing the elements of Schwinger’s basis for unitary quantum operators is endowed with a structure of symplectic type. This structure is embodied in a certain algebraic cocycle, whose main features are inherited by the symplectic form of classical phase space. In consequence, the label space may be taken as the quantum phase space: It plays, in the quantum case, the same role played by phase space in classical mechanics, some differences coming inevitably from its nonlinear character.
TL;DR: In this article, the authors discuss the transport of quantum states on quasi-energy surfaces of periodically driven systems and establish their non-trivial structure and experimental consequences pertaining to adiabatic transport and Landau-Zener transitions among Floquet states.
Abstract: We discuss the transport of quantum states on quasi-energy surfaces of periodically driven systems and establish their non-trivial structure. The latter is shown to be caused by diabatic transitions at lines of narrow avoided crossings. Some experimental consequences pertaining to adiabatic transport and Landau-Zener transitions among Floquet states are briefly sketched On traite des holonomies quantiques sur des surfaces de quasi-energie de systemes soumis a une excitation periodique, et on etablit leur topologie globale non triviale. On montre que cette derniere est causee par des transitions diabatiques entre niveaux au passage d'anti-croisements serres. On donne brievement quelques consequences experimentales concernant le transport adiabatique et les transitions de Landau-Zener entre etats de Floquet
TL;DR: In this article, the authors considered the problem of finding, for a given pair of states on C*-algebras, a joint extension to A¯¯¯¯1 ⊗ A¯¯¯¯2 and A¯¯2 ⊆ A¯¯¯¯3, and compared the necessary and sufficient criteria for extensibility in terms of Bell's inequalities.
Abstract: The problem is considered of finding, for a given pair of states on C
*-algebras A
1 ⊗ A
2 and A
2 ⊗ A
3, a joint extension to A
1 ⊗ A
2 ⊗ A
3. The fact that, in contrast to classical probability, such an extension may fail to exist, is related to the fact that different convex decompositions of the same quantum state need not have a common refinement. Improved necessary criteria for extensibility in terms of Bell's inequalities are derived, and are compared to the necessary and sufficient criteria, as well as to entropic bounds in the simplest case.
TL;DR: In this article, the time behavior of quantum states ruled by Hamiltonians linear in the SU(2), SU(1,1), and SU(3) generators in terms of the Cayley-Klein parameters, originally introduced in classical mechanics, was analyzed.
Abstract: In this paper the time behavior of quantum states ruled by Hamiltonians linear in the SU(2), SU(1,1), and SU(3) generators in terms of the Cayley–Klein parameters, originally introduced in classical mechanics is analyzed. Also pointed out is the link between the Cayley–Klein parameters and the Wei–Norman ordering functions, exploited in the context of the Schrodinger representation.