Longitudinal quantum beam tomography

Abstract

We propose an experiment to determine the density operator for the longitudinal quantum state of an atomic beam. The method is based on tomographic reconstruction of the Wigner function via a set of measured probability distributions for the phase-space rotated position operator. The time evolution of the Wigner function in free space effectively performs the required phase-space rotation. We propose a state-selective time-dependent technique for measuring longitudinal probability distributions.     

Entanglement energetics in the ground state

Abstract

We show how many-body ground state entanglement information may be extracted from sub-system energy measurements at zero temperature. A precise relation between entanglement and energy fluctuations is demonstrated in the weak coupling limit. Examples are given with the two-state system and the harmonic oscillator, and energy probability distributions are calculated. Comparisons made with recent qubit experiments show this type of measurement provides another method to quantify entanglement with the environment.     

Phase Properties of a Strong Field Interacting with Many Atoms with and Without Initial Atomic Coherences

Abstract

The phase distributions of an initially strong, coherent, single-mode field interacting with one, two, three and four identical atoms with and without initial atomic coherences using the Pegg-Barnett Hermitian phase operator formalism have been examined. A number of interesting features of the phase distributions are revealed. A link between the coincidences of the peaks in the phase probability distribution and the revivals in the two-atom case is also shown.     

Performance of binary DS‐SSMA communications through Nakagami fading channel

Abstract

A binary asynchronous direct sequence spread spectrum multiple access system through Nakagami's m‐distributed channel is considered for non‐diversity receptions. Effects of fading and multiple access interferences on the average error probability are investigated. Approximation method to the average error probability is evaluated in two steps based on the moments of multiple access interferences and Nakagami distributions. Gauss quadrature rule is applied to evaluate the conditional probability conditioned on a fixed m‐distributed fading amplitude of the desired signal. Average error probability is then evaluated by the trapezoidal integration which integrates the conditional probability and the m‐distributed probability density function of the desired signal. This method provides a good approximation to the average error probability when the number of simultaneous users is large. Numerical results for the pseudorandom codes of code length 31 and Gold codes of code length 31 and 127 are presented.     

Ground state cooling,quantum state engineering and study of decoherence of ions in Paul traps

Abstract

We investigate single ions of ⁴⁰Ca⁺ in Paul traps for quantum information processing. Superpositions of the S_½ electronic ground state and the metastable D_5/2; state are used to implement a qubit. Laser light on the S_½ ? D_5/2 transition is used for the manipulation of the ion's quantum state. We apply sideband cooling to the ion and reach the ground state of vibration with up to 99.9% probability. Starting from this Fock state (n = 0), we demonstrate coherent quantum state manipulation. A large number of Rabi oscillations and a ms-coherence time is observed. Motional heating is measured to be as low as one vibrational quantum in 190ms. We also report on ground state cooling of two ions.     

Two-mode Squeezed Pair Coherent States

Abstract

The properties of states generated by the application of the two-mode squeeze operator to the pair coherent states are studied. These states are the two-mode analogues of the single-mode squeezed states generated by the application of the single-mode squeeze operator to an ordinary coherent state. In the present case there are correlations between the modes and strong non-classical properties are to be expected. We study the statistical properties of the photon number distributions, squeezing, violations of the Cauchy-Schwartz inequality, quasiprobability distributions and the phase distributions.     

Conditional generation of non-classical states in a non-degenerate two-photon micromaser: Single-mode fock states preparation. II

Abstract

A conditional generation of single-mode Fock states in the framework of a non-degenerate two-photon micromaser theory is reported. The exact expression for the probability of success of the experiment is obtained. We show that it is possible to conjugate experimentally interesting values of this probability, with the generation of number states having a controllable high intensity. This objective is reached by constructing analytically detailed rules about the cavity state at t = 0 as well as the atom–field interaction times as functions of the available operating conditions. These rules play a central role in our Fock-state-building process, leading to an essential countering of the Stark-shift-induced detuning effects. The practical reliability of the proposal is carefully discussed from several points of view. Some possible applicative potentialities of our scheme are briefly pointed out.     

Call for Papers

Abstract

In a previous paper it was shown that the distribution of measured values for a retrodictively optimal simultaneous measurement of position and momentum is always given by the initial state Husimi function. This result is now generalized to retrodictively optimal simultaneous measurements of an arbitrary pair of rotated quadratures ? _{θ 1} and [pcirc] _{θ 2}. It is shown, that given any such measurement, it is possible to find another such measurement, informationally equivalent to the first, for which the axes defined by the two quadratures are perpendicular. It is further shown that the distribution of measured values for such a measurement belongs to the class of generalized Husimi functions most recently discussed by Wünsche and Büzek. The class consists of the subset of Wódkiewicz's operational probability distributions for which the filter reference state is a squeezed vacuum state.     

Quality quandaries: Combining engineering and statistics to assess the probability of an event

KEY POINT

This article illustrates how to combine engineering and statistical models and propagate the distributions of model inputs to estimate the probability of an event with uncertainty.     

A holographic interferometry study of natural convection in a fully‐partitioned air‐filled enclosure

Abstract

The technique of real‐time holographic interferometry is used in the present study to study natural convection in a fully‐partitioned air‐filled square enclosure. Transient and steady‐state temperature distributions in separated subenclosures are visualized for a Rayleigh number between 2.5×10⁵ and 8.4×10⁵ with a centrally‐located conducting partitions. Steady‐state experimental results are found to be in reasonably good agreement with the numerical predictions. Moreover, the experimental observations during the transient one‐sided heating processes indicate that the presence of a conducting partition can provide a good buffer against a sudden external disturbance to the enclosure.     

Homodyne tomography of classical and non-classical light

Abstract

States with explicit quantum character, such as squeezed vacuum and bright squeezed light, as well as coherent states and incoherent superpositions of coherent states were generated and analysed by tomographical methods. Wigner functions, photon-number distributions, density matrices and phase distributions were reconstructed with high accuracy. Features such as photon number oscillations, sub-Poissonian and super-Poissonian photon statistics, bifurcations of the phase distribution, and loss of coherence were observed, demonstrating the usefulness of quantum state reconstruction as an analysing tool in quantum optics experiments.     

Accounting for randomness in measurement and sampling in studying cancer cell population dynamics

Knowing the expected temporal evolution of the proportion of different cell types in sample tissues gives an indication about the progression of the disease and its possible response to drugs. Such systems have been modelled using Markov processes. We here consider an experimentally realistic scenario in which transition probabilities are estimated from noisy cell population size measurements. Using aggregated data of FACS measurements, we develop MMSE and ML estimators and formulate two problems to find the minimum number of required samples and measurements to guarantee the accuracy of predicted population sizes. Our numerical results show that the convergence mechanism of transition probabilities and steady states differ widely from the real values if one uses the standard deterministic approach for noisy measurements. This provides support for our argument that for the analysis of FACS data one should consider the observed state as a random variable. The second problem we address is about the consequences of estimating the probability of a cell being in a particular state from measurements of small population of cells. We show how the uncertainty arising from small sample sizes can be captured by a distribution for the state probability.Inspec keywords: cancer, tumours, cellular biophysics, biomedical measurement, Gaussian distribution, maximum likelihood estimation, mean square error methods, hidden Markov models, fluorescence, random processes, convergence of numerical methodsOther keywords: cancer cell population dynamics, malignant tumours, tissue samples, normal tissue cells, disease, drugs, Markov process, cell population size measurement, hidden Markov model, noisy measurement, state transition probability, fluorescence‐activated cell sorting measurement, minimum mean square error estimator, maximum likelihood estimator, transition probability matrix, noise distributions, Gaussian distributions, MMSE, convergence mechanism, standard deterministic approach, stochastic phenomena, random variable     

On tomographic reconstruction of the quantum state of a two-mode light field

Abstract

We consider the state reconstruction of an optical two-mode light field from sum quadrature distributions measured with a single balanced homodyne detector. New explicit formulas for the pattern functions necessary to reconstruct the density matrix of the two-mode field in the photon-number basis are derived. Moreover, an expression of the measured quadature distribution in terms of the two-mode normally ordered moments is given and the determination of the moments from it is discussed.     

Retrodictive quantum optical state engineering

Abstract

Although it has been known for some time that quantum mechanics can be formulated in a way that treats prediction and retrodiction on an equal footing, most attention in engineering quantum states has been devoted to predictive states, that is, states associated with a preparation event. Retrodictive states, which are associated with a measurement event and propagate backwards in time, are also useful, however. In this paper it is shown how any retrodictive state of light that can be written to a good approximation as a finite superposition of photon number states can be generated by an optical multiport device. The composition of the state is adjusted by controlling predictive coherent input states. It is shown how the probability of successful state generation can be optimized by adjusting the multiport device and also a versatile configuration that is useful for generating a range of states is examined.     

Simulations of continuum coherent states and its use in quantum cryptographic systems

Abstract

The continuum states formalism is suitable for field quantization in optical fibre; however, they are harder to use than discrete states. On the other hand, a Hermitian phase operator can be defined only in a finite dimensional space. We approximated a coherent continuum state by a finite tensor product of coherent states, each one defined in a finite dimensional space. Using this, in the correct limit, we were able to obtain some statistical properties of the photon number and phase of the continuum coherent states from the probability density functions of the individual, finite dimensional, coherent states. Then, we performed a simulation of the BB84 protocol, using the continuum coherent states, in a fibre interferometer commonly used in quantum cryptography. We observed the fluctuations of the mean photon number in the pulses that arrive at Bob, which occurs in the practical system, introduced by the statistical property of the simulation.     

Highly Excited Hydrogen in Strong D.C. Electric Fields: Atomic Engineering

Abstract

We excite atomic hydrogen from the ground state via a three-photon process to high-lying excited states in the presence of strong d.c. electric fields. The external field is used to manipulate, control, and design specific atomic structures. We can construct nearly ‘one-dimensional’ atoms whose electronic distributions are highly extended along the field, and which may have enormous electric dipole moments (‘giant-dipole atoms’).     

Relation between the Glauber–Sudarshan and Kirkwood–Rihaczek distribution functions

Abstract

The Kirkwood–Rihaczek quasiprobability distribution is written as a vacuum state expectation value of squeeze-like operators and the density matrix. We do this, by writing the position eigenstates as a squeezing-like action on the vacuum. This allows us to give a relation between the Glauber–Sudarshan and Kirkwood–Rihaczek quasiprobability distributions.     

Quantum Electrodynamics of a Rydberg Atom Making Two-photon Transitions in the Binomial State of the Field in a Lossless Cavity

Abstract

The dynamic and statistical properties of a system of an effective two-level atom making two-photon transitions in the binomial state of the field in a lossless cavity are discussed. The binomial state enables the study of the development of the phenomenon of collapses and revivals of the Rabi oscillations as the field state is changed from a pure number state to a coherent state. This is because the binomial state, which is a pure number state in one limit, develops into a coherent state as some parameters are changed appropriately. The effect of Stark shifts arising due to the transitions to virtual levels are also investigated.     

Nonequilibrium phase transitions induced by external noise in distributed systems

A formalism is proposed to describe nonequilibrium phase transitions induced by external multiplicative noise in distributed systems. This approach can reduce the problem to an investigation of a regular differential equation whose roots correspond to possible phase states in the system. By means of this theory the relative probability of the existence of one state can be compared with another and the number of possible states identified, and the genesis of the system under the action of fluctuations of the external medium can be traced. Pis’ma Zh. Tekh. Fiz. 25, 91–95 (February 26, 1999)     

Performance evaluation of a finite queue with random routing

Abstract

In previous papers [1–3], the steady‐state behavior of a finite queue which accepts batch Poisson inputs and receives service operating in the synchronous mode was studied. Analysis was successfully completed via the application of the Residue theorem in complex variables. This paper extends the work to include the effect of routing. Two types of random routing are considered in this paper. Results obtained include state‐transition probability, blocking probability, delay, and throughput. Validity of analysis has been verified by computer simulation.