Showing papers on "Quantum state published in 1996"

Observing the Progressive Decoherence of the 'Meter' in a Quantum Measurement

Abstract: A mesoscopic superposition of quantum states involving radiation fields with classically distinct phases was created and its progressive decoherence observed. The experiment involved Rydberg atoms interacting one at a time with a few photon coherent field trapped in a high $Q$ microwave cavity. The mesoscopic superposition was the equivalent of an `` $\mathrm{atom}+\mathrm{measuring}\mathrm{apparatus}$'' system in which the ``meter'' was pointing simultaneously towards two different directions---a ``Schr\"odinger cat.'' The decoherence phenomenon transforming this superposition into a statistical mixture was observed while it unfolded, providing a direct insight into a process at the heart of quantum measurement.

On Gravity's Role in Quantum State Reduction

Abstract: The stability of a quantum superposition of two different stationary mass distributions is examined, where the perturbing effect of each distribution on the space-time structure is taken into account, in accordance with the principles of general relativity. It is argued that the definition of the time-translation operator for the superposed space-times involves an inherent ill-definedness, leading to an essential uncertainty in the energy of the superposed state which, in the Newtonian limit, is proportional to the gravitational self-energyEΔ of the difference between the two mass distributions. This is consistent with a suggested finite lifetime of the order of ħ/EΔ for the superposed state, in agreement with a certain proposal made by the author for a gravitationally induced spontaneous quantum state reduction, and with closely related earlier suggestions by Diosi and by Ghirardiet al.

Semiclassicality and decoherence of cosmological perturbations

Abstract: Transition to the semiclassical behaviour and the decoherence process for inhomogeneous perturbations generated from the vacuum state during an inflationary stage in the early Universe are considered in both the Heisenberg and the Schrodinger representations to show explicitly that both approaches lead to the same prediction: the equivalence of these quantum perturbations to classical perturbations having stochastic Gaussian amplitudes and belonging to the quasi-isotropic mode. This equivalence and the decoherence are achieved once the exponentially small (in terms of the squeezing parameter ) decaying mode is neglected. In the quasi-classical limit , the perturbation mode functions can be made real by a time-independent phase rotation; this is shown to be equivalent to a fixed relation between squeezing angle and phase for all modes in the squeezed-state formalism. Though the present state of the gravitational wave background is not a squeezed quantum state in the strict sense and the squeezing parameters loose their direct meaning due to interaction with the environment and other processes, the standard predictions for the rms values of the perturbations generated during inflation are not affected by these mechanisms (at least, for scales of interest in cosmological applications). This stochastic background still occupies a small part of phase space.

Experimental Determination of the Motional Quantum State of a Trapped Atom

Abstract: We reconstruct the density matrices and Wigner functions for various quantum states of motion of a harmonically bound ${}^{9}{\mathrm{Be}}^{+}$ ion. We apply coherent displacements of different amplitudes and phases to the input state and measure the number state populations. Using novel reconstruction schemes we independently determine both the density matrix in the number state basis and the Wigner function. These reconstructions are sensitive indicators of decoherence in the system.

Fault-tolerant quantum computation

Abstract: Recently, it was realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties of realizing quantum computation is that decoherence tends to destroy the information in a superposition of states in a quantum computer, thus making long computations impossible. A futher difficulty is that inaccuracies in quantum state transformations throughout the computation accumulate, rendering the output of long computations unreliable. It was previously known that a quantum circuit with t gates could tolerate O(1/t) amounts of inaccuracy and decoherence per gate. We show, for any quantum computation with t gates, how to build a polynomial size quantum circuit that can tolerate O(1/(log t)^c) amounts of inaccuracy and decoherence per gate, for some constant c. We do this by showing how to compute using quantum error correcting codes. These codes were previously known to provide resistance to errors while storing and transmitting quantum data.

Arbitrary control of a quantum electromagnetic field

Abstract: We present a cavity QED interaction which forces the ground state of a cavity field mode to evolve into an arbitrary quantum state at a prechosen time ${t}^{*}$. This method does not involve either atom-field state entanglement or the projections characteristic of quantum measurement.

Conscious events as orchestrated space-time selections

Abstract: What is consciousness? Some philosophers have contended that "qualia," or an experiential medium from which consciousness is derived, exists as a fundamental component of reality. Whitehead, for example, described the universe as being comprised of "occasions of experience." To examine this possibility scientifically, the very nature of physical reality must be re-examined. We must come to terms with the physics of space-time--as is described by Einstein's general theory of relativity--and its relation to the fundamental theory of matter--as described by quantum theory. This leads us to employ a new physics of objective reduction: " OR" which appeals to a form of quantum gravity to provide a useful description of fundamental processes at the quantum/classical borderline (Penrose, 1994; 1996). Within the OR scheme, we consider that consciousness occurs if an appropriately organized system is able to develop and maintain quantum coherent superposition until a specific "objective" criterion (a threshold related to quantum gravity) is reached; the coherent system then self-reduces (objective reduction: OR). We contend that this type of objective self-collapse introduces non-computability, an essential feature of consciousness. OR is taken as an instantaneous event--the climax of a self-organizing process in fundamental space-time--and a candidate for a conscious Whitehead "occasion" of experience. How could an OR process occur in the brain, be coupled to neural activities, and account for other features of consciousness? We nominate an OR process with the requisite characteristics to be occurring in cytoskeletal microtubules within the brain's neurons (Penrose and Hameroff, 1995; Hameroff and Penrose, 1995; 1996). In this model, quantum-superposed states develop in microtubule subunit proteins ("tubulins"), remain coherent and recruit more superposed tubulins until a mass-time-energy threshold (related to quantum gravity) is reached. At that point, self-collapse, or objective reduction (OR) abruptly occurs. We equate the pre-reduction, coherent superposition ("quantum computing") phase with pre-conscious processes, and each instantaneous (and non-computable) OR, or self-collapse, with a discrete conscious event. Sequences of OR events give rise to a "stream" of consciousness. Microtubule-associated-proteins can "tune" the quantum oscillations of the coherent superposed states; the OR is thus self-organized, or "orchestrated" ("Orch OR"). Each Orch OR event selects (non-computably) microtubule subunit states which regulate synaptic/neural functions using classical signaling. The quantum gravity threshold for self-collapse is relevant to consciousness, according to our arguments, because macroscopic superposed quantum states each have their own space-time geometries (Penrose, 1994; 1996). These geometries are also superposed, and in some way "separated," but when sufficiently separated, the superposition of space-time geometries becomes significantly unstable, and reduce to a single universe state. Quantum gravity determines the limits of the instability; we contend that the actual choice of state made by Nature is non-computable. Thus each Orch OR event is a self-selection of space-time geometry, coupled to the brain through microtubules and other biomolecules. If conscious experience is intimately connected with the very physics underlying space-time structure, then Orch OR in microtubules indeed provides us with a completely new and uniquely promising perspective on the hard problem of consciousness.

Geometries of quantum states

Abstract: The quantum analog of the Fisher information metric of a probability simplex is searched and several Riemannian metrics on the set of positive definite density matrices are studied. Some of them appeared in the literature in connection with Cramer–Rao‐type inequalities or the generalization of the Berry phase to mixed states. They are shown to be stochastically monotone here. All stochastically monotone Riemannian metrics are characterized by means of operator monotone functions and it is proven that there exist a maximal and a minimal among them. A class of metrics can be extended to pure states and a constant multiple of the Fubini–Study metric appears in the extension.

V Photon Wave Function

Abstract: Publisher Summary This chapter describes the photon wave function, and explains the basic properties of a well-defined mathematical object—a six-component function of space-time variables—that describes the quantum state of the photon. The most essential property that does not hold for the photon wave function is that the argument of the wave function cannot be directly associated with the position operator of the photon. The position operator for the photon simply does not exist. However, one should remember that for massive particles also, the true position operator exists only in the nonrelativistic approximation. The concept of localization associated with the Newton-Wigner position operator is not relativistically invariant. The photon wave function is not restricted to the wave mechanics of photons. The same wave functions also appear as mode functions in the expansion of the electromagnetic field operators.

Quantum Statistics of the Squeezed Vacuum by Measurement of the Density Matrix in the Number State Representation.

Abstract: We report the reconstruction of the quantum state of squeezed vacuum generated by a continuous-wave optical parametric amplifier. Homodyne detection and tomographic reconstruction methods were used to obtain the density matrix in the Fock (number state) representation. The photon number distribution exhibits odd-even oscillations, a manifestation of the photon pair production in the second-order nonlinear medium.

Chaotic analytic zero points: exact statistics for those of a random spin state

Abstract: A natural statistical ensemble of 2J points on the unit sphere can be associated, via the Majorana representation, with a random quantum state of spin J, and an exact expression is obtained here for the general k point correlation function in this ensemble. The pair correlation in the large-J limit takes the relatively simple form where and is the angular separation of the pair of points on the sphere. It appears (from the numerical work of others) that, in this limit, these statistics are typical of the zero points of analytic functions associated with chaotic quantum dynamical systems.

Eckardt frame theory of interacting electrons in quantum dots

Abstract: A transformation to a moving frame (the Eckardt frame) is used to study the quantum states of interacting electrons in parabolic quantum dots in the presence of a perpendicular magnetic field. The approach is motivated by examining ground-state pair-correlation functions obtained by exact diagonalization. The main results concern the physical nature of the electron states and the origin of magic numbers. Some of the states are found to be localized about a single minimum of the potential energy. They have well-defined symmetry and are physically analogous to molecules. They are treated approximately by antisymmetrizing Eckardt frame rotational-vibrational states. This approach leads to selection rules that predict all the magic angular momentum and spin combinations found in previous numerical work. In addition, it enables the ground-state energy and low-lying excitations of the molecular states to be calculated to high accuracy. Analytic results for three electrons agree very well with the results of exact diagonalization. States that are not localized about a single minimum are also studied. They do not have distinct spatial symmetry and occur only when selection rules and conservation laws allow tunneling between states localized on different minima. These states appear to be small system precursors of fractional quantum Hall liquids. \textcopyright{} 1996 The American Physical Society.

Photon Chopping: New Way to Measure the Quantum State of Light

Abstract: We propose the use of a balanced $2N$-port as a technique to measure the pure quantum state of a single-mode light field. In our scheme the coincidence signals of simple, realistic photodetectors are recorded at the output of the $2N$-port. We show that applying different arrangements both the modulus and the phase of the coefficients in a finite superposition state can be measured. In particular, the photon statistics can be so measured with currently available devices.

Quantum mechanical three-dimensional wavepacket study of the Li+HF --> LiF+H reaction

Abstract: A three‐dimensional time‐dependent quantum mechanical wavepacket method is used to calculate the state‐to‐state reaction probabilities at zero total angular momentum for the Li + HF → LiF +H reaction. Reaction probabilities starting from several different initial HF vibrational–rotational states (v=0,j=0,1,2) and going to all possible open channels are computed over a wide range of energies. A single computation of the wavepacket dynamics yields reaction probabilities from a specific initial quantum state of the reactants to all possible final states over a wide range of energies. The energy dependence of the reaction probabilities shows a broad background structure on which resonances of varying widths are superimposed. Sharp resonance features seem to dominate particularly at low product translational energies. There are marked changes in the energy dependence of the reaction probabilities for different initial or final diatom rotational quantum numbers, but it is noticeable that, for both reactants and...

Concatenated Quantum Codes

Abstract: One of the main problems for the future of practical quantum computing is to stabilize the computation against unwanted interactions with the environment and imperfections in the applied operations. Existing proposals for quantum memories and quantum channels require gates with asymptotically zero error to store or transmit an input quantum state for arbitrarily long times or distances with fixed error. In this report a method is given which has the property that to store or transmit a qubit with maximum error $\epsilon$ requires gates with error at most $c\epsilon$ and storage or channel elements with error at most $\epsilon$, independent of how long we wish to store the state or how far we wish to transmit it. The method relies on using concatenated quantum codes with hierarchically implemented recovery operations. The overhead of the method is polynomial in the time of storage or the distance of the transmission. Rigorous and heuristic lower bounds for the constant $c$ are given.

Quantum-to-classical Transition of Cosmological Perturbations for Non-vacuum Initial States

Abstract: Transition from quantum to semiclassical behaviour and loss of quantum coherence for inhomogeneous perturbations generated from a non-vacuum initial state in the early Universe is considered in the Heisenberg and the Schrodinger representations, as well as using the Wigner function. We show explicitly that these three approaches lead to the same prediction in the limit of large squeezing (i.e. when the squeezing parameter $|r_k|\to \infty$): each two-modes quantum state (k, -k) of these perturbations is equivalent to a classical perturbation that has a stochastic amplitude, obeying a non-gaussian statistics which depends on the initial state, and that belongs to the quasi-isotropic mode (i.e. it possesses a fixed phase). The Wigner function is not everywhere positive for any finite $r_k$, hence its interpretation as a classical distribution function in phase space is impossible without some coarse graining procedure. However, this does not affect the transition to semiclassical behaviour since the Wigner function becomes concentrated near a classical trajectory in phase space when $|r_k|\to \infty$ even without coarse graining. Deviations of the statistics of the perturbations in real space from a Gaussian one lie below the cosmic variance level for the N-particles initial states with N=N(|k|) but may be observable for other initial states without statistical isotropy or with correlations between different k modes. As a way to look for this effect, it is proposed to measure the kurtosis of the angular fluctuations of the cosmic microwave background temperature.

Squeezed phonon states: Modulating quantum fluctuations of atomic displacements.

Abstract: We study squeezed quantum states of phonons, which allow the possibility of modulating the quantum fluctuations of atomic displacements below the zero-point quantum noise level of coherent phonon states. We calculate the corresponding expectation values and fluctuations of both the atomic displacement and lattice amplitude operators, and also investigate the possibility of generating squeezed phonon states using a three-phonon parametric amplification process based on phonon-phonon interactions. Furthermore, we also propose a detection scheme based on reflectivity measurements.

Theory of an atom laser

Abstract: Superconductivity, superfluidity, Bose-Einstein condensation, and laser amplification are all examples of a general mechanism involving the stimulated transfer of bosons into a specific quantum state When the occupation number of the state is large, this mechanism may generate a macroscopic coherence for the state amplitude In this paper, we demonstrate that the stimulated transfer of bosonic atoms into a given state of an optical or a magnetic trap can give rise to a coherent atomic source in analogy with the photon laser and we present a general model for such a device

Time-dependent quantum systems and the invariant Hermitian operator

Abstract: We study the time evolution of quantum systems with a time-dependent Hamiltonian given by a linear combination of SU(1,1) and SU(2) generators. The invariant Hermitian operator is constructed in the same manner as for both the SU(1,1) and SU(2) systems. With the help of the invariant Hermitian operator we obtain not only the exact solutions of the Schr\"odinger equation but also the time-evolution operator. The adiabatic and nonadiabatic Berry phases are calculated with the exact solutions. \textcopyright{} 1996 The American Physical Society.

Self-consistent relaxation-time models in quantum mechanics

Abstract: . This paper is concerned with the relaxation-time von Neumann- Poisson (or quantum Liouville-Poisson) equation in three spatial dimensions which describes the self-consistent time evolution of an open quantum me- chanical system that includes some relaxation mechanism. This model and the equivalent relaxation-time Wigner-Poisson system play an important role in the simulation of quantum semiconductor devices. For initial density matrices with finite kinetic energy, we prove that this problem, formulated in the space of Hermitian trace class operators, admits a unique global strong solution. A key ingredient for our analysis is a new generalization of the Lieb-Thirring inequality for density matrix operators.

Construction of quantum states of the radiation field by discrete coherent-state superpositions

Abstract: An efficient method of quantum state engineering based on discrete superpositions of coherent states is presented. A systematic method is developed for obtaining optimized superpositions from the one-dimensional representation of the desired state. It is shown that superposition of even a small number of coherent states put along a straight line or on a circle in phase space can approximate nonclassical field states with a high degree of accuracy. An experimental scheme is proposed for generating equidistant coherent-state superpositions on a circle with arbitrary coefficients. \textcopyright{} 1996 The American Physical Society.

Geometry of Quantum Statistical Inference.

Abstract: An efficient geometric formulation of the problem of parameter estimation is developed, based on Hilbert space geometry. This theory, which allows for a transparent transition between classical and quantum statistical inference, is then applied to the analysis of exponential families of distributions (of relevance to statistical mechanics) and quantum mechanical evolutions. The extension to quantum theory is achieved by the introduction of a complex structure on the given real Hilbert space. We find a set of higher order corrections to the parameter estimation variance lower bound, which are potentially important in quantum mechanics, where these corrections appear as modifications to Heisenberg uncertainty relations for the determination of the parameter. [S0031-9007(96)01153-2]

NO3 Photolysis Product Channels: Quantum Yields from Observed Energy Thresholds

Abstract: The absorption of visible light by NO3 leads to three products: NO + O2, NO2 + O, and fluorescence. We report a new method for obtaining quantum yields for the NO3 molecule, using measured energy thresholds separating NO3 and its product channels. The assumptions of this model are the following: (i) NO3 internal energy (photon plus vibrations plus rotations) gives the necessary and sufficient condition to select each of the three product channels, as justified by the observed large differences in reaction times for the three products. (ii) The unresolved complexities of ground-state NO3 spectra and quantum states are approximated by standard separable ro-vibrational expressions for statistical mechanical probability functions. These results may be of interest to both physical chemists and atmospheric chemists. The NO3* vibronic precursors of the three product channels are identified. We evaluate and plot vibrational state-specific absolute quantum yields as a function of wavelength Φvib(λ) for each prod...

The wigner semi-circle law in quantum electro dynamics

Abstract: In the present paper, the basic ideas of thestochastic limit of quantum theory are applied to quantum electro-dynamics. This naturally leads to the study of a new type of quantum stochastic calculus on aHilbert module. Our main result is that in the weak coupling limit of a system composed of a free particle (electron, atom,...) interacting, via the minimal coupling, with the quantum electromagnetic field, a new type of quantum noise arises, living on a Hilbert module rather than a Hilbert space. Moreover we prove that the vacuum distribution of the limiting field operator is not Gaussian, as usual, but a nonlinear deformation of the Wigner semi-circle law. A third new object arising from the present theory, is the so-calledinteracting Fock space. A kind of Fock space in which then quanta, in then-particle space, are not independent, but interact. The origin of all these new features is that we do not introduce the dipole approximation, but we keep the exponential response term, coupling the electron to the quantum electromagnetic field. This produces a nonlinear interaction among all the modes of the limit master field (quantum noise) whose explicit expression, that we find, can be considered as a nonlinear generalization of theFermi golden rule.