We theoretically examine two-color photoassociation of a Bose-Einstein condensate, focusing on the role of rogue decoherence in the formation of macroscopic atom-molecule superpositions. Rogue dissociation occurs when two zero-momentum condensate atoms are photoassociated into a molecule, which then dissociates into a pair of atoms of equal-and-opposite momentum, instead of dissociating back to the zero-momentum condensate. As a source of decoherence that may damp quantum correlations in the condensates, rogue dissociation is an obstacle to the formation of a macroscopic atom-molecule superposition. We study rogue decoherence in a setup which, without decoherence, would yield a macroscopic atom-molecule superposition, and find that the most favorable conditions for said superpositions are a density $\rho \sim {10}^{12}{\mathrm{cm}}^{-3}$ and temperature $T\sim 0.1\mathrm{nK}$.

Condensation of atom pairs with finite total momentum is expected in a portion of the phase diagram of a two-component fermionic cold-atom system. This unusual condensate can be identified by detecting the exotic higher-Landau-level (HLL) vortex lattice states it can form when rotated. With this motivation, we have solved the linearized gap equations of a polarized cold-atom system in a Landau-level basis to predict experimental circumstances under which HLL vortex lattice states occur.

The dynamical evolution of a Bose-Einstein condensate trapped in a one-dimensional lattice potential is investigated theoretically in the framework of the Bose-Hubbard model. The emphasis is set on the far-from-equilibrium evolution in a case where the gas is strongly interacting. This is realized by an appropriate choice of the parameters in the Hamiltonian, and by starting with an initial state, where one lattice well contains a Bose-Einstein condensate while all other wells are empty. Oscillations of the condensate as well as noncondensate fractions of the gas between the different sites of the lattice are found to be damped as a consequence of the collisional interactions between the atoms. Functional integral techniques involving self-consistently determined mean fields as well as two-point correlation functions are used to derive the two-particle-irreducible (2PI) effective action. The action is expanded in inverse powers of the number of field components $\mathcal{N}$, and the dynamic equations are derived from it to next-to-leading order in this expansion. This approach reaches considerably beyond the Hartree-Fock-Bogoliubov mean-field theory, and its results are compared to the exact quantum dynamics obtained by Rey et al. [Phys. Rev. A 69, 033610 (2004)] for small atom numbers.

We perform a detailed numerical analysis of Fabry-Perot cavities used for state-of-the-art laser stabilization. Elastic deformation of Fabry-Perot cavities with various shapes and mounting methods is quantitatively analyzed using finite-element analysis. We show that with a suitable choice of mounting schemes it is feasible to minimize the susceptibility of the resonator length to vibrational perturbations. This investigation offers detailed information on stable optical cavities that may benefit the development of ultrastable optical local oscillators in optical atomic clocks and precision measurements probing the fundamental laws of physics.

Quantum-mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Rényi entropies. The proof of these inequalities requires the use of the exact expression for the $(p,q)$-norm of the Fourier transformation derived by Babenko and Beckner. Analogous uncertainty relations are derived for angle and angular momentum and also for a pair of complementary observables in $N$-level systems. All these uncertainty relations become more attractive when expressed in terms of the symmetrized Rényi entropies.

We present a simple method to obtain an upper bound on the achievable secret key rate in quantum key distribution (QKD) protocols that use only unidirectional classical communication during the public-discussion phase. This method is based on a necessary precondition for one-way secret key distillation; the legitimate users need to prove that there exists no quantum state having a symmetric extension that is compatible with the available measurements results. The main advantage of the obtained upper bound is that it can be formulated as a semidefinite program, which can be efficiently solved. We illustrate our results by analyzing two well-known qubit-based QKD protocols: the four-state protocol and the six-state protocol.

Estimating the fidelity of state preparation in multiqubit systems is generally a time-consuming task. Nevertheless, this complexity can be reduced if the desired state can be characterized by certain symmetries measurable with the corresponding experimental setup. In this paper we give simple expressions to estimate the fidelity of multiqubit state preparation for rotational-invariant, stabilizer, and generalized coherent states. We specifically discuss the GHZ-type and W-type states, and obtain efficiently measurable lower bounds for the fidelity. We use these techniques to estimate the fidelity of a quantum simulation of an Ising-like interaction model using two trapped ions. These results are directly applicable to experiments using fidelity-based entanglement witnesses, such as quantum simulations and quantum computation.

In the first two papers in this series, we developed a method for studying electron-hydrogen scattering that does not use partial-wave analysis. We constructed an ansatz for the wave function in both the static and static exchange approximations and calculated the full scattering amplitude. Here we go beyond the static exchange approximation, and include correlation in the wave function via a modified polarized orbital. This correlation function provides a significant improvement over the static exchange approximation: the resultant elastic scattering amplitudes are in very good agreement with fully converged partial-wave calculations for electron-hydrogen scattering. A fully variational modification of this approach is discussed in the conclusion.

We investigate the collective excitations of a one-dimensional Bose-Einstein condensate with repulsive interaction between atoms in a quadratic plus quartic trap. Using variational approaches, the coupled equations of motions for the center-of-mass coordinate of the condensate and its width are derived. Then, two low-energy excitation modes are obtained analytically. The frequency shift induced by the anharmonic distortion, and the collapse and revival of the collective excitations originating from the nonlinear coupling between the two modes, are discussed.

We show the possibility of transparency and soliton effects for an intense pulse propagating in a $V$-type medium in which two upper resonant sublevels experience fast field-induced decay due to incoherent coupling to an upper lying state or continuum. The transparency arises as a result of the combined action of population trapping on the sublevels leading to interference suppression of the relaxation channel, and coherent Rabi cycling induced by the laser field.

Based on (i) the spectral resolution definition of the momentum operator, (ii) the linearity of correspondence between physical observables and quantum Hermitian operators, (iii) the definition of conjugate coordinate-momentum variables in classical mechanics, and (iv) the invariance of the classical Hamiltonian to canonical transformations (transformations that change from one set of conjugate variables to another), we show that the $[\widehat{x},\widehat{p}]$ coordinate-momentum commutator must have the value $ih$ where $h$ is a real nonzero number (which we can identify with the experimentally determined $\hslash$). The results are then extended to include all generalized coordinates and their conjugate momenta as well as the Cartesian special-relativistic case.

We realize NMR optimal tomography of a single qubit by coupling it to an ancilla, letting them interact, and measuring properties of the joint system. Among other advantages, this approach reduces the number of counting rates that are necessary for establishing tomography of the qubit, due to the fact that this number (equal to 4) is equal to the number of real parameters of the density matrix. Connections with the discrete Wigner distribution are emphasized and discussed.

Standard security proofs of quantum-key-distribution (QKD) protocols often rely on symmetry arguments. In this paper, we prove the security of a three-state protocol that does not possess rotational symmetry. The three-state QKD protocol we consider involves three qubit states, where the first two states $\mid 0_z⟩$ and $\mid 1_z⟩$ can contribute to key generation, and the third state $\mid +⟩=(\mid 0_z⟩+\mid 1_z⟩)∕\sqrt{2}$ is for channel estimation. This protocol has been proposed and implemented experimentally in some frequency-based QKD systems where the three states can be prepared easily. Thus, by founding on the security of this three-state protocol, we prove that these QKD schemes are, in fact, unconditionally secure against any attacks allowed by quantum mechanics. The main task in our proof is to upper bound the phase error rate of the qubits given the bit error rates observed. Unconditional security can then be proved not only for the ideal case of a single-photon source and perfect detectors, but also for the realistic case of a phase-randomized weak coherent light source and imperfect threshold detectors. Our result in the phase error rate upper bound is independent of the loss in the channel. Also, we compare the three-state protocol with the Bennett-Brassard 1984 (BB84) protocol. For the single-photon source case, our result proves that the BB84 protocol strictly tolerates a higher quantum bit error rate than the three-state protocol, while for the coherent-source case, the BB84 protocol achieves a higher key generation rate and secure distance than the three-state protocol when a decoy-state method is used.

We establish bounds to the necessary resource consumption when building up cluster states for one-way computing using probabilistic gates. Emphasis is put on state preparation with linear optical gates, as the probabilistic character is unavoidable here. We identify rigorous general bounds to the necessary consumption of initially available maximally entangled pairs when building up one-dimensional cluster states with individually acting linear optical quantum gates, entangled pairs, and vacuum modes. As the known linear optics gates have a limited maximum success probability, as we show, this amounts to finding the optimal classical strategy of fusing pieces of linear cluster states. A formal notion of classical configurations and strategies is introduced for probabilistic nonfaulty gates. We study the asymptotic performance of strategies that can be simply described, and prove ultimate bounds to the performance of the globally optimal strategy. The arguments employ methods of random walks and convex optimization. This optimal strategy is also the one that requires the shortest storage time, and necessitates the fewest invocations of probabilistic gates. For two-dimensional cluster states, we find, for any elementary success probability, an essentially deterministic preparation of a cluster state with quadratic, hence optimal, asymptotic scaling in the use of entangled pairs. We also identify a percolation effect in state preparation, in that from a threshold probability on, almost all preparations will be either successful or fail. We outline the implications on linear optical architectures and fault-tolerant computations.

Optical lattices with one atom on each site and interacting via cold controlled collisions provide an efficient way to entangle a large number of qubits with high fidelity. It has already been demonstrated experimentally that this approach is especially suited for the generation of cluster states [O. Mandel et al., Nature 425, 937 (2003)] which reduce the resource requirement for quantum computing to the ability to perform single-qubit rotations and qubit read out. In this paper, we describe how to implement these rotations in one-dimensional and two-dimensional optical lattices without having to address the atoms individually with a laser field.

We formulate a quasi-Hermitian delta-shell pseudopotential for higher partial wave scattering, and show that any such potential must have an energy-dependent regularization. The quasi-Hermiticity of the Hamiltonian leads to a complete set of biorthogonal wave functions that can be used as a basis to expand and diagonalize other two-body Hamiltonians. We demonstrate this procedure for the case of ultracold atoms in a polarization-gradient optical lattice, interacting pairwise when two atoms are transported together from separated lattice sites. Here the pseudopotential depends explicitly on the trapping potential. Additionally, we calculate the location of trap-induced resonances for higher partial waves, which occur when a molecular eigenstate is shifted to resonance with a trap eigenstate. We verify the accuracy of the pseudopotential approach using a toy model in which a square well acts as the true interaction potential, and see excellent agreement.

The molecular dynamics of Autler-Townes (AT) splitting in a multiphoton resonance ionization spectrum is numerically simulated using the time-dependent wave packet method for a rotating ${\mathrm{Na}}_2$ molecule with a linearly polarized laser pulse. Employing the Fourier grid method and Legendre polynomials as basis functions, the initial wave packet is directly propagated using the split operator method. Wave packet dynamics simulations demonstrate that the AT splitting results from rapid Rabi oscillations induced by an ultrashort intense laser pulse in rovibrational coherent states that belong to different electronic terms. But Rabi oscillations will be damped because of the effects of rotation and alignment of the molecule in laser fields. The AT splitting in a photoelectron spectrum could be observed for a well-aligned molecule with sufficiently rapid Rabi oscillations. Only an adequately short laser pulse can induce AT splitting in a photoelectron spectrum. The effect of initial rotational temperature on the molecular dynamics is also studied.

The intensity-intensity correlation function of the resonance fluorescence light of two two-level atoms driven by a resonant standing-wave laser field is examined. Our aim is to gain information on the distance between the two atoms from observables accessible in experiments. For this, we numerically solve the time-evolution equations of the system and calculate the steady-state intensity-intensity correlation by using the Laplace transform and quantum regression theory. By varying the interatomic distance from about half a wavelength down to small fractions of a wavelength, we show that the correlation function exhibits characteristic properties for different distance ranges. Based on these results, we propose a scheme to obtain interatomic distance information from the power spectrum of the correlation function, which allows us to extract the desired distance information over a wide range of distances with high accuracy.

We derive expressions for the coupling coefficients for electromagnetic four-wave mixing in the nonlinear quantum vacuum. An experimental setup for detection of elastic photon-photon scattering is suggested, where three incoming laser pulses collide and generate a fourth wave with a new frequency and direction of propagation. An expression for the number of scattered photons is derived and, using beam parameters for the Astra Gemini system at the Rutherford Appleton Laboratory, it is found that the signal can reach detectable levels. Problems with shot-to-shot reproducibility are reviewed, and the magnitude of the noise arising from competing scattering processes is estimated. It is found that detection of elastic photon-photon scattering may be achieved.