Motivated by the production of strong optical forces on atoms, we have done numerical studies of adiabatic rapid passage in light that is both frequency and amplitude modulated in the form of chirped pulses, and we found unanticipated regularities. We have quantified these regularities in terms of a periodic Hamiltonian, and obtained a result similar to the Bloch theorem, but in the time domain. This led to further numerical studies and a quantitative description of the behavior of an atom under multiply repetitive sweeps.

We study the response of a Bose-Einstein condensate to a periodic modulation of the depth of an optical lattice. Using Gross-Pitaevskii theory, we show that a modulation at frequency $\Omega$ drives the parametric excitation of Bogoliubov modes with frequency $\Omega ∕2$. The ensuing nonlinear dynamics leads to a rapid broadening of the momentum distribution and a consequent large increase of the condensate size after free expansion. We show that this process does not require the presence of a large condensate depletion. Our results reproduce the main features of the spectrum measured in the superfluid phase by Stöferle et al. [Phys. Rev. Lett. 92, 130403 (2004)].

We propose a feasible scheme of quantum state storage and manipulation via electromagnetically induced transparency in flexibly united multiensembles of three-level atoms. For different atomic array configurations, one can properly steer the signal and the control lights to generate different forms of atomic entanglement within the framework of linear optics. These results opens up new possibility for the future design of quantum memory devices by using, e.g., an atomic grid.

Minima in the generalized oscillator strength (GOS) and the convergence of the GOS to the first Born approximation (FBA) limit for the Ba $6s{}^{1}S\to 6p{}^{1}P$ optically allowed transition are investigated. The random-phase approximation with exchange, which takes into account correlation effects among the atomic electrons themselves, and the convergent close-coupling (CCC) approximation are used for the calculations. We find the following. (1) The GOS as a function of the momentum transfer squared $K^2$ is characterized by a complex structure of multiple minima, significantly different in the two approximations and approaches the high-energy FBA limit only at small $K^2$ values (less than about $0.5\mathrm{a.u.}$). (2) The number of minima calculated in the CCC approximation increases with increase in energy, but does not correspond to the number obtained in the FBA, even at high energy $\sim 1\mathrm{keV}$. The CCC and FBA minima are in general not directly related. The FBA minima, except for the first, do not correspond to physical observables at these energies. (3) At high energy the interaction between the incident electron and the target remains significant, resulting in slowing down the convergence of the CCC GOS to the corresponding nonrelativistic FBA results.

We derive the atom-molecule theory for an atomic gas near a broad Feshbach resonance, where the energy dependence of the atom-molecule coupling becomes crucial for understanding experimental results. We show how our many-body theory incorporates the two-atom physics exactly. In particular, we calculate the magnetic moment of a two-component gas of ${}^6\mathrm{Li}$ atoms for a wide range of magnetic fields near the broad Feshbach resonance at about $834\mathrm{G}$. We find excellent agreement with the experiment of Jochim et al. [Phys. Rev. Lett. 91, 240402 (2003)].

We study a Bose-Einstein condensate with attractive interactions in a one-dimensional ring and show that the ground state is well described by the superposition of bright solitons. A position measurement of some atoms gives rise to the state reduction of the soliton position, which increases the condensate fraction. The bunched many-body ground state is well approximated by a simple variational wave function.

The inner-shell excitation spectra of krypton $3d$ electrons were measured at scattering angles of 0° and 4° by a fast-electron energy-loss spectrometer at an incident energy of 2.5 keV with an energy resolution better than 80 meV. Some interesting optically forbidden transitions were observed and the natural widths of the optically allowed and optically forbidden transitions were analyzed. It shows that the natural widths for the resonances having the same core hole are nearly equal, no matter whether they are optically allowed, optically forbidden, or different members of a Rydberg series.

We propose a practical, scalable, and efficient scheme for quantum computation using spatially separated matter qubits and single-photon interference effects. The qubit systems can be nitrogen-vacancy centers in diamond, Pauli-blockade quantum dots with an excess electron, or trapped ions with optical transitions, which are each placed in a cavity and subsequently entangled using a double-heralded single-photon detection scheme. The fidelity of the resulting entanglement is extremely robust against the most important errors such as detector loss, spontaneous emission, and mismatch of cavity parameters. We demonstrate how this entangling operation can be used to efficiently generate cluster states of many qubits, which, together with single-qubit operations and readout, can be used to implement universal quantum computation. Existing experimental parameters indicate that high-fidelity clusters can be generated with a moderate constant overhead.

Optimal implementation of quantum gates is crucial for designing a quantum computer. The necessary condition for optimal construction of a two-qubit unitary operation is obtained. It can be proved that the $B$ gate is the unique gate that can construct a two-qubit universal circuit with only two applications, i.e., this condition is also sufficient in the case of two applications of the elementary two-qubit gate. It is also shown that many perfect entanglers cannot simulate an arbitrary two-qubit gate with only three applications. We show how a two-qubit gate’s construction power is related to the construction power of its mirror gate, and introduce a specific kind of two-qubit entangling gate, i.e., a super controlled gate, which can construct an arbitrary two-qubit gate by three applications.

The information capacities and “distillability” of a quantum channel are studied in the presence of auxiliary resources. These include prior entanglement shared between the sender and receiver and free classical bits of forward and backward communication. Inequalities and trade-off curves are derived. In particular an alternative proof is given that in the absence of feedback and shared entanglement, forward classical communication does not increase the quantum capacity of a channel.

This work analyzes a key distribution system presented earlier [Phys. Rev. A 68, 052307 (2003)] using elements of information theory. Mutual information functions describing the information content shared by Alice and Bob, the legitimate users, and between Alice and Eve, the attacker, are obtained. These results support the original claims that the overall security level to be obtained with the $M$-ry key distribution system can be made arbitrarily high and thus secure for any practical application. Effects of losses and amplifiers in the optical channel are also analyzed.

We study multipartite entanglement measures for a one-dimensional Ising chain that is capable of showing both integrable and nonintegrable behavior. This model includes the kicked transverse Ising model, which we solve exactly using the Jordan-Wigner transform, as well as nonintegrable and mixing regimes. The cluster states arise as a special case and we show that while one measure of entanglement is large, another measure can be exponentially small, while symmetrizing these states with respect to up and down spins produces those with large entanglement content uniformly. We also calculate exactly some entanglement measures for the nontrivial but integrable case of the kicked transverse Ising model. In the nonintegrable case we begin on extensive numerical studies that show that large multipartite entanglement is accompanied by diminishing two-body correlations, and that time averaged multipartite entanglement measures can be enhanced in nonintegrable systems.

A scheme is presented for realizing two-atom quantum logic gates with a single resonant interaction. The scheme does not use the cavity mode as the data bus and only requires a single resonant interaction of the atoms with a cavity mode. Thus the scheme is very simple and the interaction time is very short, which is important in view of decoherence. Quantum information can be directly transferred from one atom to another atom using this idea. The scheme can also be generalized to the ion trap system.

The dynamical behavior of the entanglement and the squeezing in the system of two ions trapped in a lossy optical cavity is discussed, in which the vibrational mode of the first ion is coupled to the cavity field via a linear-mixing interaction and the vibrational mode of the second ion is coupled to the cavity field via an effective parametric interaction, respectively. It is found that when the effective strength $r_1$ of the coupling between the first ion and the cavity field is stronger than the strength $r_2$ of the coupling between the second ion and the cavity field, the motional state of the two ions develops into a robust two-mode mixed Gaussian entangled state and the two-mode squeezing of phonons appears. But the entanglement between the cavity mode and the vibrational mode of the second ion can only happen periodically in a small time range. When $r_1<r_2$, only the entanglement between the two vibrational modes appears but the two-mode squeezing does not exist. And the entanglement between the cavity mode and the motional mode of the second ion can also take place in a small time range.

We have investigated the two-photon nonlinearity attained by a finite-sized excitonic system placed inside of a cavity, paying attention to the dependence on the system size $N$. The two-photon nonlinearity is evaluated by utilizing semiclassical optical responses. In the quantum-dot limit, the excitonic system behaves as a single two-level system with an enhanced coupling to the cavity mode. In the bulk limit, the nonlinear phase shift decreases as $N$ is increased, proportionally to $N^{-1∕2}$.

We propose a symmetrization procedure to beat decoherence for oscillator-assisted quantum gate operations. The enacted symmetry is related to the global geometric features of qubits transformation based on ancillary oscillator modes, e.g., phonons in an ion-trap system. It is shown that the devised multicircuit symmetrized evolution endows the system with a twofold resilience against decoherence: insensitivity to thermal fluctuations and quantum dissipation.

For a solvable pure-decoherence model, we confirm by an explicit model calculation that the decay of entanglement of two two-state systems (two qubits) is approximately governed by the product of the suppression factors describing decoherence of the subsystems, provided that they are subject to uncorrelated sources of quantum noise. This demonstrates an important physical property that separated open quantum systems can evolve quantum mechanically on time scales larger than the times for which they remain entangled.

The energy gap is calculated for a ground-state quantum computer circuit. It is found that, when implementing a quantum algorithm by Hamiltonians containing only pairwise interaction, the inverse of energy gap is proportional to $N^{4k}$, where $N$ is the number of bits involved in the problem, and $N^k$ is the number of control operations performed in a standard quantum paradigm.

The macroscopic electromagnetic field is quantized in the presence of a uniformly moving permeable dielectric medium. We begin with the Maxwell-Minkowski equations, and the fields are quantized with the help of the Green function scheme. It is shown that for a homogeneous material, though the medium is assumed to be isotropic in its rest frame, it displays anisotropic character for the observer who detects the field observables in the laboratory frame. The field operators are expressed in terms of two independent infinite sets of bosonic field operators. Special attention is paid to the vacuum field fluctuation in moving media.

It is demonstrated, using a Liouville formalism, that the relative motion of two atoms can result in the emission of photons and conversely that photons can be absorbed to excite the relative translational motion. The mechanism responsible for the energy transfer between the radiation field and the translational motion of the atoms is a dynamic version of the long-range Casimir-Polder interaction between two fixed atoms. The phenomenon is analogous to the dynamic Casimir effect discussed for moving macro- (or meso)scopic objects and we term it the dynamic Casimir-Polder effect. The absorption or emission is a two-photon process and we find that the transition probability is proportional to the spectral density of a correlation function involving the relative translational motion of two atoms. An energy transfer only occurs for photons with energies smaller than or of the same magnitude as the thermal energy. The effect provides a microscopic mechanism for establishing thermal equilibrium between the radiation field and a gas. A sufficiently large volume of gas would be perceived as a black-body radiator. Applications of the dynamic Casimir-Polder effect might be found in the microscopic description of the cosmic low-temperature black-body radiation.