Non-classical Properties of Even and Odd Coherent States

Abstract

We present a detailed discussion of even and odd coherent states defined as eigenstates of the single mode two-photon annihilation operator a ². We study the non-classical properties such as squeezing, higher-order squeezing, and photon antibunching. Also discussed are the various quantum quasiprobability distributions, namely the P function, which is shown to be highly singular, the Q function, and the Wigner, which can take on negative values for these states. Finally, we present a discussion of a possible mechanism for the generation of such states based on the competition between parametric amplification and the incoherent losses from two-photon resonant absorption.     

Squeezing in Correlated Quantum Systems

Abstract

We discuss the connection between quantum correlations and squeezing in simple quantum optical systems. We illustrate this connection by a study of two-mode states of light produced by parametric down-conversion and similar two-photon processes. The intermode correlations in these systems are shown to be responsible for modifications in photon-number sum and difference operators, and for squeezing in the superpositions of the two modes. The disappearance of the diagonal coherent-state quasiprobability function P(α) when non-classical light properties are important is noted, and alternative and better-behaved Wigner functions and coherent-state expectation Q-functions for the two-mode system are developed.     

The information role of entanglement and interference operators in Shor quantum algorithm gate dynamics

Abstract

Shor algorithm dynamics of quantum computation states are analysed from the classical and the quantum information theory points of view. The Shannon entropy is interpreted as the degree of information accessibility through measurement, while the von Neumann entropy is employed to measure the quantum information of entanglement. The intelligence of a state with respect to a subset of qubits is defined. The intelligence of a state is maximal if the gap between the Shannon and the von Neumann entropy for the chosen result qubits is minimal. We prove that the quantum Fourier transform creates maximally intelligent states with respect to the first n qubits for Shor's problem, since it annihilates the gap between the classical and quantum entropies for the first n qubits of every output state.     

Quantum phase measurements and non-classical polarization states of light

Abstract

In our paper we consider the non-classical behaviour of both the Hermitian (observable) Stokes parameters of light and the phase difference of two modes that describe the quantum polarization states of optical field. To characterize the degree of polarization of light we introduce a new quantity taking into account the quantum properties of different quantum states of two orthogonally polarized modes. The problem of determination of the phase difference in two modes of optical field for the quantum polarization states of light is discussed. To describe in general such a quantum field we introduce two pairs of the phase operators: the phase angles for the Stokes parameters of light in a three-dimensional picture of the Poincaré sphere. We also consider a special type of the eight-port polarization interferometer (polarimeter) for simultaneous homodyne detection of both the Stokes parameters of light and the polarization phase operators and their fluctuations as well. Using an anisotropic (spatioperiodic) Kerr-like nonlinear medium associated with the polarization interferometer we could generate and also observe the polarization-squeezed phase states of light. The fluctuations in the phase difference between two orthogonally polarized modes for these non-classical states are less than the fluctuations for light in coherent state.     

The Interaction of Displaced Number State and Squeezed Number State Fields with Two-level Atoms

Abstract

The time-evolution of a single two-level atom in a single-mode high-Q cavity is sensitive to the quantum fluctuations of the cavity radiation field and to its photon statistics: this sensitivity is realizable experimentally in the Rydberg atom micromaser. We study the effects of the interaction of a two-level atom with two new non-classical radiation fields: the squeezed number state and the displaced number state realizable by nonlinear and linear transformations of field number states which have an initially precise occupation number. The time-varying field fluctuations caused by the atomic interaction are described using the Q-function quasi-probability.     

Detector efficiency limits on quantum improvement

Abstract

Although the National Institute of Standards and Technology has measured the intrinsic quantum efficiency of Si and InGaAs avalanche photo diode (APD) materials to be above 98% by building an efficient compound detector, commercially available devices have efficiencies ranging between 15 and 75%. This means bandwidth, dark current, cost, and other factors are more important than quantum efficiency for existing applications. For non-classical correlated photon applications, the system's correlated signal-to-noise ratio is proportional to (ηN)^½ /(1 ? η)^½, rather than the classical signal-to-noise (ηN)^½. Consequently, the detector design trade space must be re-evaluated. This paper systematically examines the generic detection process, lays out the considerations needed for designing detectors for non-classical applications, and identifies the ultimate physical limits on quantum efficiency.     

Optical Measurement Accuracy in the Case of Non-classical Light

Abstract

The influence of optical elements on the statistical properties of the input radiation is analysed by quantum-theoretical means for a representative optical arrangement consisting of beam splitters as well as for various types of grating spectrometers. In particular non-classical light states are studied. Optimum conditions for the maintenance of the signal-to-noise ratio of sub-Poissonian input radiation are derived.     

Experimental preparation and measurement of quantum states of motion of a trapped atom

Abstract

We report the creation and full determination of several quantum states of motion of a ⁹Be⁺ ion bound in a RF (Paul) trap. The states are coherently prepared from an ion which has been initially laser cooled to the zero-point of motion. We create states having both classical and non-classical character including thermal, number, coherent, squeezed, and ?Schrödinger cat‘ states. The motional quantum state is fully reconstructed using two novel schemes that determine the density matrix in the number state basis or the Wigner function. Our techniques allow well controlled experiments decoherence and related phenomena on the quantum-classical borderline.     

Phase-sensitive non-classicality criteria for phase-independent quantum states

A recently introduced hierarchy of necessary and sufficient conditions for non-classicality of a quantum state [Th. Richter and W. Vogel, Phys. Rev. Lett. 89 283601 (2002)] is applied to the characterization of phase-insensitive quantum states. Even under such conditions it may be important to analyse the relation between different phase values in the quadrature distributions in order to demonstrate the non-classical nature of the state under study.     

Vibrational superposition states without rotating wave approximation

Abstract

We propose a scheme to generate superpositions of coherent states for the vibrational motion of a laser-cooled trapped ion. It is based on the interaction with a standing wave making use of the counter-rotating terms, i.e. not applying the rotating wave approximation. We also show that the same scheme can be exploited for quantum state measurement, i.e. with the same scheme non-classical states may be reconstructed.     

Practical Implications of Quantum Noise

Abstract

This paper gives an introduction to quantum noise and the limits it places on optical measurements. Squeezed states of light, and their representation on phasor diagrams, are then introduced. The use of squeezed states to improve interferometric measurements is described. Quantum non-demolition measurements are discussed, with particular reference to their use in high sensitivity absorption experiments. Finally, sources of some other types of non-classical light and possible experiments making use of these sources are considered.     

Influence of Kerr-like medium on the dynamics of a two-mode Raman coupled model

Abstract

We study the quantum dynamics of an effective two-level atom interacting with two modes via Raman process inside an ideal cavity in the presence of Kerr non-linearity. The cavity modes interact both with the atom as well as the Kerr-like medium. The unitary transformation method presented here, not only solves the time-dependent problem, but also provides the eigensolutions of the interacting Hamiltonian at the same time. We study the atomic-population dynamics and the dynamics of the photon statistics in the two cavity modes. The influence of the Kerr-like medium on the statistics of the field is explored and it is observed that Kerr medium introduces antibunching in mode 1 and this effect is enhanced by a stronger interaction with the non-linear medium. In the high non-linear coupling regime anticorrelated beam become correlated. Kerr medium also introduces non-classical correlation between the two modes.     

Reconstruction of quantum states of spin systems via the Jaynes principle of maximum entropy

Abstract

We apply the Jaynes principle of maximum entropy for the partial reconstruction of correlated spin states. We determine the minimum set of observables which is necessary for the complete reconstruction of the most correlated states of systems composed of spins 1/2 (e.g. the Bell and the Greenberger-Horne-Zeilinger states). We investigate to what extent an incomplete measurement can reveal non-classical features of correlated spin states.     

Quantum teleportation with number states and beam splitters

Abstract

Quantum communication is a new and fascinating area in telecommunications that provides new ways of communication without classical counterparts. At the centre of this theory is quantum entanglement, a powerful and enigmatic property shown by some composite quantum systems. In this paper, the entanglement produced by sending of number states through a beam splitter is studied. The property entangled is the parity of the number of photons of the number states at the beam splitter's outputs. The decoherence is taken into account through the losses. The entanglement of pure and mixed states at the output of the beam splitter is calculated and some protocols for quantum teleportation for bipartite (C₂ ? C₂) and tripartite (C₂ ? C₂ ? C₂), systems are described.     

Generating non-classical light inside an optical cavity by depositing photons

The creation of non-classical states of light is an interesting problem, that we solve sending atoms through an optical cavity. We show that it is possible to add or subtract many photons from a cavity field by interacting it resonantly with a two-level atom. The atom, after entangling with the field inside the cavity and exiting it, may be measured in one of the Schmidt states, producing a multiphoton process (in the sense that can add or annihilate more photons than a single transition allows), i.e. adding or subtracting several photons from the cavity field. By plotting the quadratures and the Husimi Q-function, we also show that the non-classical state produced by such measurements is a squeezed state.     

Continuous photodetection of resonance fluorescence

Abstract

The concept of photodetection as a continuous quantum measurement introduced by Srinivas and Davies is extended to the detection of resonance fluorescence. This is a new approach to an old subject. This is also a new development in continuous photodetection in the sense that a fermion rather than the traditional boson field is the subject of monitoring. The superoperators for the no-count and the one-count processes are postulated, following the examples of Srinivas and Davies. The probability for the m-count process is then derived on the basis of these postulates. The first two factorial moments of the photon-number distribution are calculated, which are then used to evaluate the non-classical effects in resonance fluorescence. A parameter slightly different from Mandel's is found to be more suitable indicator of photon antibunching in the transient state.     

Population trapping with quantized fields in two-channel models of atomic excitation

Abstract

In this paper, we study several models of two-channel atomic excitation involving quantized fields and search for field states that result in the trapping of the atomic population in a single bare state. This trapping is a result of quantum interference between the two channels. We study the following models: a two-level atom resonantly interacting with two quantized field modes, a two-level atom with competing one and three photon transitions, and a Raman coupled model containing both Stokes and anti-Stokes fields. We find a great variety of trapping states of the field, some of the states being highly non-classical. The effects of dissipation on the stability of the trapping states are discussed and a method for generating some of the states is presented.     

A New Quantum Formalism for Damping and Gain in Harmonic Oscillators

Abstract

A new formulation of loss or gain in the quantum theory of harmonic oscillators is put forward using a non-passive reactive circuit which can be readily quantized. The analysis is based on the electrical circuit theory and demonstrates how a circuit, with negative inductance ? L _n and negative capacitance ? C _n, coupled to a conventional harmonic oscillator circuit, of positive inductance L and positive capacitance C, can act as a source or sink of energy and allow for both gain and loss. Classically this series circuit is indistinguishable in its transients from either a + G or ? G conductance shunted across a main LC oscillator circuit. However, unlike the resistive circuit, this coupled circuit can be quantized, maintaining the uncertainty principle. A two-valued solution is found, dependent on whether the circuits are in a state to receive energy or a state to absorb energy. A full correspondence, including second-order frequency shifts, is found between the quantum and the classical solutions with states which are appropriate to thermodynamic equilibrium of a conductance at a temperature T as well as to the classical-like coherent states. While the accessible mode in the + L + C circuit does not exhibit any squeezing directly, the system as a whole is an example of two-mode squeezing discussed by other authors.     

Information Transfer with Two-state Two-particle Quantum Systems

Abstract

Any future quantum information machine will contain unitary operators and entangled particle states. The Hilbert space describing the action of the quantum information machine separates into a bosonic and a fermionic sector. Because the bosonic sector is of higher dimension, it is always possible to encode more information into a multiboson state than into a multifermion state, given the same complexity, that is unitary representation, of the quantum information machine. This is explicitly studied for the case of two particles defined in two modes. There the beam splitter is a generic representation of any U(2) matrix, and it has recently been shown that one can realize any N-dimensional unitary operator by successive application of such two-dimensional operators. The two-boson two-mode Hilbert space is of dimension three, and thus one can encode log₂3 = 1·57 bits of information into such an entangled state. Finally, some explicit schemes for creating and detecting the three possible, two-photon, two-mode states spanning the bosonic Bell basis are given.