In this paper I investigate the usability of the characteristic functions for the description of the dynamics of open quantum systems focussing on non-Lindblad-type master equations. I consider, as an example, a non-Markovian generalized master equation containing a memory kernel which may lead to nonphysical time evolutions characterized by negative values of the density matrix diagonal elements [S. M. Barnett and S. Stenholm, Phys. Rev. A 64, 033808 (2001)]. The main result of the paper is to demonstrate that there exist situations in which the symmetrically ordered characteristic function is perfectly well-defined while the corresponding density matrix loses positivity. Therefore, nonphysical situations may not show up in the characteristic function. As a consequence, the characteristic function cannot be considered an alternative complete description of the non-Lindblad dynamics.

Feedback control is expected to considerably protect quantum states against decoherence caused by interaction between the system and environment. Especially, Markovian feedback scheme developed by Wiseman can modify the properties of decoherence and eventually recover the purity of the steady state of the corresponding master equation. This paper provides a condition for which the modified master equation has a pure steady state. By applying this condition to a two-qubit system, we obtain a complete parametrization of the feedback Hamiltonian such that the steady state becomes a maximally entangled state.

We describe an approach to quantum control of the quasiparticle excitations in a trapped Bose-Einstein condensate based on adiabatic and diabatic changes in the trap anisotropy. We describe our approach in the context of the Landau-Zener transition at the avoided crossings in the quasiparticle excitation spectrum. We find also that there can be population oscillation between different modes at the specific aspect ratios of the trapping potential at which the mode energies are almost degenerate. These effects may have implications in the expansion of an excited condensate as well as the dynamics of a moving condensate in an atomic waveguide with a varying width.

Promotion of quantum theory from a theory of measurement to a theory of reality requires an unambiguous specification of the ensemble of realizable states (and each state’s probability of realization). Although not yet achieved within the framework of standard quantum theory, it has been achieved within the framework of the continuous spontaneous localization (CSL) wave-function collapse model. In CSL, a classical random field $w(\mathbf{x},t)$ interacts with quantum particles. The state vector corresponding to each $w(\mathbf{x},t)$ is a realizable state. In this paper, I consider a previously presented model, which is predictively equivalent to CSL. In this completely quantized collapse (CQC) model, the classical random field is quantized. It is represented by the operator $W(\mathbf{x},t)$ which satisfies $[W(\mathbf{x},t),W({\mathbf{x}}^{\prime },t^{\prime })]=0$. The ensemble of realizable states is described by a single state vector, the “ensemble vector.” Each superposed state which comprises the ensemble vector at time $t$ is the direct product of an eigenstate of $W(\mathbf{x},t^{\prime })$, for all $\mathbf{x}$ and for $0⩽t^{\prime }⩽t$, and the CSL state corresponding to that eigenvalue. These states never interfere (they satisfy a superselection rule at any time), they only branch, so the ensemble vector may be considered to be, as Schrödinger put it, a “catalog” of the realizable states. In this context, many different interpretations (e.g., many worlds, environmental decoherence, consistent histories, modal interpretation) may be satisfactorily applied. Using this description, a long-standing problem is resolved, where the energy comes from the particles gain due to the narrowing of their wave packets by the collapse mechanism. It is shown how to define the energy of the random field and its energy of interaction with particles so that total energy is conserved for the ensemble of realizable states. As a by-product, since the random-field energy spectrum is unbounded, its canonical conjugate, a self-adjoint time operator, can be discussed. Finally, CSL is a phenomenological description, whose connection to, or derivation from, more conventional physics has not yet appeared. We suggest that, because CQC is fully quantized, it is a natural framework for replacement of the classical field $w(\mathbf{x},t)$ of CSL by a quantized physical entity. Two illustrative examples are given.

We analyze a model system of fermions in a harmonic oscillator potential under the influence of a dissipative environment: The fermions are subject to a fluctuating force deriving from a bath of harmonic oscillators. This represents an extension of the well-known Caldeira-Leggett model to the case of many fermions. Using the method of bosonization, we calculate one- and two-particle Green’s functions of the fermions. We discuss the relaxation of a single extra particle added above the Fermi sea, considering also dephasing of a particle added in a coherent superposition of states. The consequences of the separation of center-of-mass and relative motion, the Pauli principle, and the bath-induced effective interaction are discussed. Finally, we extend our analysis to a more generic coupling between system and bath, which results in complete thermalization of the system.

We study the computation power of lattices composed of two-dimensional systems (qubits) on which translationally invariant global two-qubit gates can be performed. We show that if a specific set of six global two qubit gates can be performed and if the initial state of the lattice can be suitably chosen, then a quantum computer can be efficiently simulated.

We investigate how stabilizer theory can be used for constructing sufficient conditions for entanglement. First, we show how entanglement witnesses can be derived for a given state, provided some stabilizing operators of the state are known. These witnesses require only a small effort for an experimental implementation and are robust against noise. Second, we demonstrate that also nonlinear criteria based on uncertainty relations can be derived from stabilizing operators. These criteria can sometimes improve the witnesses by adding nonlinear correction terms. All our criteria detect states close to Greenberger-Horne-Zeilinger states, cluster and graph states. We show that similar ideas can be used to derive entanglement conditions for states which do not fit the stabilizer formalism, such as the three-qubit $W$ state. We also discuss connections between the witnesses and some Bell inequalities.

Each classical public-coin protocol for coin flipping is naturally associated with a quantum protocol for weak coin flipping. The quantum protocol is obtained by replacing classical randomness with quantum entanglement and by adding a cheat detection test in the last round that verifies the integrity of this entanglement. The set of such protocols defines a family which contains the protocol with bias 0.192 previously found by the author, as well as protocols with bias as low as $1∕6$ described herein. The family is analyzed by identifying a set of optimal protocols for every number of messages. In the end, tight lower bounds for the bias are obtained which prove that $1∕6$ is optimal for all protocols within the family.

Recently the problem of unambiguous state discrimination of mixed quantum states has attracted much attention. So far, bounds on the optimum success probability have been derived [T. Rudolph, R. W. Spekkens, and P. S. Turner, Phys. Rev. A 68, 010301(R) (2003)]. For two mixed states they are given in terms of the fidelity. Here we give tighter bounds as well as necessary and sufficient conditions for two mixed states to reach these bounds. Moreover we construct the corresponding optimal measurement strategies. With this result, we provide analytical solutions for unambiguous discrimination of a class of generic mixed states. This goes beyond known results which are all reducible to some pure state case. Additionally, we show that examples exist where the bounds cannot be reached.

We study possible realizations of generalized quantum measurements on measurement-assisted programmable quantum processors. We focus our attention on the realization of von Neumann measurements and informationally complete positive-operator-valued measures. Nielsen and Chuang [Phys. Rev. Lett. 79, 321 (1997)] have shown that two unitary transformations implementable by the same programmable processor require mutually orthogonal states. We show that two different von Neumann measurements can be encoded into nonorthogonal program states. Nevertheless, given the dimension of a Hilbert space of the program register the number of implementable von Neumann measurements is still limited. As an example of a programmable processor we use the so-called quantum-information distributor.

We have measured relative cross sections and fragmentation branching ratios for proton–carbon monoxide collisions over a wide velocity range from 0.63 to 23.7 a.u. (i.e., $E_p$ of 10 keV to 14 MeV) using a coincidence time-of-flight technique. For low projectile velocity, where electron capture by the projectile becomes important, this process is separated from ionization by projectile charge-state analysis. Our measurements of ${\mathrm{CO}}^{2+}$ production resolve differences between previous measurements, but our multiple-ionization cross-section measurements differ significantly from recent measurements by Siegmann et al. [Phys. Rev. A 66, 052701 (2002)]. The observed kinetic-energy release from dissociating channels varies slowly as the incident proton velocity changes, and in general is not compatible with a simple Coulomb explosion picture.

We present calculations for the double photoionization (with excitation) and the triple photoionization of Li and Be. We extend and more fully discuss the previous calculations made for Li by Colgan et al. [Phys. Rev. Lett. 93, 053201 (2004)] and present calculations for Be. The Be triple photoionization cross sections are compared with previous double shake-off model calculations of Kheifets and Bray [J. Phys. B 36, L211 (2003)], and our calculations are found to be significantly lower.

The importance of second-order effects in the projectile-target interaction, channel coupling in the ejected-electron–residual-ion interaction, and multiconfiguration effects in the target description is investigated for electron-impact ionization of argon. For incident projectile energies of 200 and $113.5\mathrm{eV}$, a scattering angle of 15°, and ejected-electron energies between 2 and $20\mathrm{eV}$, we find a strong sensitivity of the theoretical predictions to the target structure, channel coupling, and the proper treatment of nonlocal exchange. In some cases, accounting for these effects seems more important than extending a local-exchange, single-configuration distorted-wave theory by including the accurate three-body Coulomb asymptotic boundary condition. Despite encouraging improvement in agreement between our predictions and recent experimental results in some cases, severe discrepancies remain in others. More experimental data, preferably absolute but at least cross-normalized to each other for a variety of kinematic conditions, seem necessary to further guide ongoing theoretical efforts.

Clusters of the divalent metals magnesium, cadmium, and zinc have been grown in ultracold helium nanodroplets and studied by high-resolution mass spectrometry, with a special emphasis on magnesium. The mass spectra of all materials show similar characteristic features independent of the chosen ionization technique—i.e., electron impact ionization as well as nanosecond and femtosecond multiphoton excitation. In the lower-size range the abundance distributions can be explained by an electronic shell structure. The associated electron delocalization—i.e., metallic bonding—is found to set in at about $N=20$ atoms. For ${\mathrm{Mg}}_N$ we have resolved crossings of electronic levels at the highest-occupied molecular orbital which result in additional magic numbers compared to the alkali metals: e.g., ${\mathrm{Mg}}_{40}$ with 80 electrons. This specific electronic shell structure is also present in the intensity pattern of doubly charged ${\mathrm{Mg}}_N$. For larger clusters $(N⩾92)$ a coexistence of electronic shell effects and geometrical packing is observed and a clear signature of icosahedral structure is present beyond $N⩾147$.

We have measured the ionization rate for CO molecules exposed to intense $30\mathrm{fsec}$ $780\mathrm{nm}$ laser pulses as a function of the angle between the molecular and laser polarization axes. Nonionizing, $70\mathrm{fsec}$ laser pulses are used to coherently prepare the molecules, preferentially aligning them for the strong-field ionization experiments. We find a 2:1 ionization-rate ratio for molecules aligned parallel or perpendicular to the ionizing field.

We have calculated $(1+1+1^{\prime })$-photon dissociation cross section of the NaH molecule from $v^{″}=0$ level of the ground $X{}^1\Sigma ^{+}$ state to the repulsive $B^1\Pi$ state via the bound $A{}^1\Sigma ^{+}$ state by using three delayed ultrashort pulses. Two delayed $4\text{femtosecond}$ pulses have been used for the first step transition to design interfering wave packets on the intermediate $A{}^1\Sigma ^{+}$ state and the third delayed ultrashort pulse (either $\delta$-function or $4\text{femtosecond}$) excites these wave packets to the dissociating state. We have shown that control over dissociation dynamics can be achieved by controlling delay between three pulses, the pulse durations, and the carrier frequencies. We have considered two values of delay between the first two $4\text{femtosecond}$ pulses for which it is possible to inhibit and enhance the deexcitation channel to the ground state and hence for these two delays the maximum of the cross section in the dissociation spectrum can be enhanced or diminished respectively for the $\delta$-function transition to the dissociating state by the third ultrashort pulse. The dissociation spectrum also depends on the delay of the third pulse. The dependence of the dissociation cross section on the delays of pulses and on the carrier frequency of the third pulse has been demonstrated for two step dissociating transition by three delayed $4\text{femtosecond}$ pulses of Gaussian shape. It has been suggested that the oscillation of dissociation cross section with time delay of the third pulse can be realized as time dependent quantum gates and the nature of quantum gates can be controlled by choosing pulses of different shape, duration, and photon energy (or carrier frequency) as well as delay between the pulses. This aspect of realization and precise control of time dependent quantum gate in light molecules by using three ultrashort pulses $\left(4\text{femtosecond}\right)$ has not been explored before.

In a condensate made of two different atomic molecular species, Onsager’s quantization condition implies that around a vortex, the velocity field cannot be the same for the two species. We explore some simple consequences of this observation. Thus, if the two condensates are in slow relative translation one over the other, the composite vortices are carried at a velocity that is a fraction of the single-species velocity. This property is valid for attractive interaction and below a critical velocity which corresponds to a saddle-node bifurcation.

A two-dimensional rapidly rotating Bose-Einstein condensate in a harmonic plus quartic trap is expected to have unusual vortex states that do not occur in a pure harmonic trap. At a critical rotation speed ${\Omega }_h$, a central hole appears in the condensate, and at some faster rotation speed ${\Omega }_g$, the system undergoes a transition to a giant vortex state with pure irrotational flow. Using a time-dependent variational analysis, we study the behavior of an annular condensate with a single concentric ring of vortices. The transition to a giant vortex state is investigated by comparing the energy of the two equilibrium states (the ring of vortices and the giant vortex) and also by studying the dynamical stability of small excitation modes of the ring of vortices.

The effect of random magnetic fields on the dissociation of ultracold molecules with Feshbach resonances is studied analytically. The dissociation spectrum and the evolution of the molecule fraction are obtained for a general form of the magnetic-field ramp and different noise properties relevant to standard experimental conditions. The results uncover the robustness against noise of some characteristics of the dissociation process, in particular, of the dependence of the mean atomic kinetic energy on the system parameters. Implications for the applicability of a method proposed to determine the width of the Feshbach resonances from the measurement of the dissociation spectrum are analyzed. Moreover, we discuss how the presence of fluctuations can affect the use of particular ramp shapes to tailor the properties of the generated atomic distribution.

We show that a plane-mirror Fabry-Perot cavity is capable of converting a spatially phase (amplitude) modulated input beam into an amplitude (phase) modulated output. For a cavity close to resonance the effect is most easily seen for negative detunings. When nonlinear elements are added to the mean-field cavity, the effect persists but acquires an intensity dependence, while the requirement of net negative dispersion remains. In addition, the output of a near-resonant nonlinear cavity can have the same type of modulation as the input, something which is impossible in the corresponding linear cavity. These results are demonstrated in cavities containing Kerr or two-level materials, as well as in optical parametric oscillators.