Qudit-type entanglement of continuous variables via weak cross-Kerr non linearity

We propose a protocol for creating arbitrary qudit state (including entangled states) with arbitrary dimensionality in continuous variable system using weak cross-Kerr nonlinearity, linear beamsplitters, detectors not resolving photon numbers, and sources of coherent states. The equation for unique determination of the used coherent states amplitudes is found. The protocol is applicable for creating entangled states at distances of 100 km using cross-Kerr nonlinearity χ ≥ χ _min ≃ 0.01 and optical fiber quantum channel.     

SU(1,1) Lie Algebra Applied to the General Time-dependent Quadratic Hamiltonian System

Exact quantum states of the time-dependent quadratic Hamiltonian system are investigated using SU(1,1) Lie algebra. We realized SU(1,1) Lie algebra by defining appropriate SU(1,1) generators and derived exact wave functions using this algebra for the system. Raising and lowering operators of SU(1,1) Lie algebra expressed by multiplying a time-constant magnitude and a time-dependent phase factor. Two kinds of the SU(1,1) coherent states, i.e., even and odd coherent states and Perelomov coherent states are studied. We applied our result to the Caldirola–Kanai oscillator. The probability density of these coherent states for the Caldirola–Kanai oscillator converged to the center as time goes by, due to the damping constant γ. All the coherent state probability densities for the driven system are somewhat deformed. PACS Numbers: 02.20.Sv, 03.65.-w, 03.65.Fd     

The<Emphasis Type="Italic">SU</Emphasis>(1,1) coherent states related to the affine group wavelets

The Perelomov coherent states ofSU(1,1) are labeled by elements of the quotient ofSU(1,1) by its rotation subgroup. Taking advantage of the fact that this quotient is isomorphic to the affine group of the real line, we are able to parameterize the coherent states by elements of that group. Such a formulation permits to find new properties of theSU(1,1) coherent states and to relate them to affine wavelets. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001.     

Mean spin direction and spin squeezing in superpositions of spin coherent states

We consider the mean spin direction (MSD) of superpositions of two spin coherent states (SCS) | ± μ〉, and superpositions of | μ〉 and | μ*〉 with a relative phase. We find that the azimuthal angle exhibits a π transition for both states when we vary the relative phase. The spin squeezing of the states, and the bosonic counterpart of the mean spin direction are also discussed.      

Feedback in the problem of distinguishing between two nonorthogonal coherent states

Feedback is proposed for distinguishing between two weak coherent states with phases differing by ∼π. The mutual nonorthogonality of such states gives rise to a discrimination error, which can be reduced by using feedback. An optical quantum channel is discussed where the input is classical information encoded in two weak coherent states. For a channel with feedback, the discrimination error probability is calculated, and the mutual entropy that quantifies the fidelity between input and output is evaluated. We find that the use of a feedback loop in a quantum communication channel can increase the mutual entropy when canonical position or photon number is measured.     

Diffraction of the wave packet of a three-level Λ atom in the field of a multifrequency standing light wave

The diffraction of the wave packet of a three-level atom in a multifrequency optical radiation field is studied. A new type of coherent beam splitter for atoms that employs the scattering of a wave packet in the field of four standing light waves with different spatial shifts is proposed on this basis. It is shown that this interaction scheme makes it possible to obtain large splittings (>100ℏk) of the wave packet of a three-level Λ atom in momentum space into only two coherent components. In addition, the atoms in these coherent components are in long-lived atomic states, which substantially simplifies the experimental implementation of such a splitter. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 6, 386–391 (25 September 1997)     

Extremum uncertainty product and sum states

We consider the states with extremum products and sums of the uncertainties in non-commuting observables. These are illustrated by two specific examples of harmonic oscillator and the angular momentum states. It shows that the coherent states of the harmonic oscillator are characterized by the minimum uncertainty sum 〈(Δq)²〉 + 〈(Δp)²〉. The extremum values of the sums and products of the uncertainties of the components of the angular momentum are also obtained.     

Photon-added coherent states for the Morse oscillator

In the paper we have constructed and investigated some properties of the Perelomov's “generalized coherent states” and photon-added coherent states for the Morse one-dimensional Hamiltonian (MO-PACSs), using the SU(2) group generators. We have found the integration measure in the resolution of unity and we have calculated some expectation values in the MO-PACSs representation. Using these states, the diagonal P-representation of the density operator is constructed as a new result for Morse potential. In addition, we have calculated some thermal expectation values for the quantum canonical diatomic gas of the Morse oscillators.     

Time Accuracy for Superposition of Coherent States in Quantum Clock Synchronization

The analysis of accuracy for arbitrary number N copies of identical prepared samples has been performed based on Bayesian framework. The time accuracies for even superposition of coherent states (SCSs) and odd SCSs could only achieve standard quantum limit for average photon number n (or α ²) is larger. The accuracies are also deduced from the approach of Cramér-Rao bound. It can be seen from the comparison that the accuracies derived from two methods in agreement with each other when n is large. The even SCSs could provide higher precision than classical coherent states in the interval 0.7≤n≤3.     

Wigner function and Bell’s inequalities for even and odd coherent states

The Wigner function and the symplectic tomogram of an entangled quantum state, which is a superposition of the photon’s coherent states (even and odd coherent states), is studied. Photon statistics and violation of Bell’s inequality for the photon state are discussed.     

Holomorphic representation of coherent states of a singular oscillator and their Darboux representation

We consider the coherent states of a singular oscillator; these states are defined to be the characteristic states of an operator that reduces the number of basis functions for a discrete spectrum to one. We use the Darboux transform to study the coherent states of a transformed Hamiltonian. We obtain an expression for measures that can be used to decompose unity. We construct a holomorphic representation for the state vectors in the space of functions holomorphic everywhere in the complex plane, including vectors for discrete spectra and coherent states. We obtain a holomorphic representation of the Darboux transformation operators. Tomsk State University. Institute of High-Energy Electronics. Siberian Division of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 46–53, February, 1998.     

Coherent states of potentials of soliton origin

The spectral properties of the most general time-dependent potentials of the soliton type described by a self-adjoint operator acting in Hilbert space are discussed. The spectral decomposition for these potentials and the quasispectral decomposition for the Darboux transformation operators are obtained. The coherent states of such systems are examined. Finally, the measure realizing the decomposition of the identity operator in the projectors on the coherent states is calculated. Zh. éksp. Teor. Fiz. 114, 1930–1943 (December 1998)     

Generation of displaced squeezed superpositions of coherent states

We study the method of generation of states that approximate superpositions of large-amplitude coherent states (SCSs) with high fidelity in free-traveling fields. Our approach is based on the representation of an arbitrary single-mode pure state, and SCSs in particular, in terms of displaced number states with an arbitrary displacement amplitude. The proposed optical scheme is based on alternation of photon additions and displacement operators (in the general case, N photon additions and N − 1 displacements are required) with a seed coherent state to generate both even and odd displaced squeezed SCSs regardless of the parity of the used photon additions. It is shown that the optical scheme studied is sensitive to the seed coherent state if the other parameters are unchanged. Output states can approximate either even squeezed SCS or odd SCS shifted relative to each other by some value. This allows constructing a local rotation operator, in particular, the Hadamard gate, which is a mainframe element for quantum computation with coherent states. We also show that three-photon additions with two intermediate displacement operators are sufficient to generate even displaced squeezed SCS with the amplitude 1.7 and fidelity more than 0.99. The effects deteriorating the quality of output states are considered.     

Exponential Mixing and Time Scales¶in Quantized Hyperbolic Maps on the Torus

We study the behaviour, in the simultaneous limits , of the Husimi and Wigner distributions of initial coherent states and position eigenstates, evolved under the quantized hyperbolic toral automorphisms and the quantized baker map. We show how the exponential mixing of the underlying dynamics manifests itself in those quantities on time scales logarithmic in . The phase space distributions of the coherent states, evolved under either of those dynamics, are shown to equidistribute on the torus in the limit , for times t between and , where γ is the Lyapounov exponent of the classical system. For times shorter than , they remain concentrated on the classical trajectory of the center of the coherent state. The behaviour of the phase space distributions of evolved position eigenstates, on the other hand, is not the same for the quantized automorphisms as for the baker map. In the first case, they equidistribute provided t→∞ as , and as long as t is shorter than . In the second case, they remain localized on the evolved initial position at all such times. Received: 1 October 1999/Accepted: 4 January 2000     

Darboux transformation of coherent states for a Lobachevski plane

A Darboux transformation of coherent states is considered for a singular oscillator. A coordinate representation and a holomorphic representation are obtained for the Darboux transformation operator and the coherent states. The Hermitian metric and the Kaler potential of the transformed system are calculated. It is established that a Darboux transformation corresponds to curvature of the phase space of the classical system. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 29–36, September, 1997.     

Entanglement in Bipartite Generalized Coherent States

Entanglement of formation in a class of bipartite generalized coherent states is discussed. It is shown that a positive parameter can be associated with these bipartite states so that the states with equal value for the parameter are of equal entanglement. For the class of states considered, the maximum possible entanglement of one ebit is attained if the value of the positive parameter is . It is shown that the entanglement of formation is one ebit when the relative phase between the composing states is π in the class of bipartite generalized coherent states considered.     

Measurement of the beam asymmetry Σ in πeta; production off the proton with the CBELSA/TAPS experiment?

In photoproduction experiments, a large number of final states yielding various resonance contributions are accessible. To extract resonance parameters via partial-wave analysis not only the measurement of differential cross-sections is necessary, but also the determination of polarization observables. At the electron accelerator ELSA (Bonn) the coherent bremsstrahlung method was used to generate a linearly polarized photon beam. Using the CBELSA/TAPS detector setup, the beam asymmetry Σ in the reaction γp → pπ⁰η was determined as a function of various masses and angles for photon energies between 970MeV and 1650MeV.     

Compact (correlated) coherent states of an electron moving in the field of a plane electromagnetic wave

Compact coherent states of the relativistic electron which satisfy the conditions of completeness and orthogonality are constructed in the field of a plane electromagnetic wave. The physical sense of the quantum parameters introduced is defined, as well as their connection with the indeterminacy of coordinates and momentum. The breakdown of the coherent state is found with respect to all possible states which correspond to various classical trajectories of a particle, and the association of the derived results with Volkov's solutions is established. Tomsk Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 45–49, February, 1993.