We study an ultracold gas of $N$ bosons trapped in a one-dimensional $M$-site optical lattice perturbed by a spatially dependent potential $g{x}^j$, where the unknown coupling strength $g$ is to be estimated. We find that the measurement uncertainty is bounded by $\Delta g\propto \frac{1}{N(M^j-1)}$. For a typical case of a linear potential, the sensitivity improves as $M^{-1}$, which is a result of multiple interferences between the sites, an advantage of multipath interferometers over two-mode setups. Next, we calculate the estimation sensitivity for a specific measurement where, after the action of the potential, the particles are released from the lattice and form an interference pattern. If the parameter is estimated by a least-squares fit of the average density to the interference pattern, the sensitivity still scales like $M^{-1}$ for linear potentials. We finally discuss the role of useful entanglement of the initial state in the lattice to beat the shot-noise limit.

The coupling of antimatter to gravity is of general interest because of conceivable cosmological consequences (“surprises”) related to dark energy and the cosmological constant. Here, we revisit the derivation of the gravitationally coupled Dirac equation and find that the prefactor of a result given previously by Brill and Wheeler [Rev. Mod. Phys. 29, 465 (1957)] for the affine connection matrix is in need of a correction. We also discuss the conversion of the curved-space Dirac equation from the so-called “East-Coast” to the “West-Coast” convention, in order to bring the gravitationally coupled Dirac equation to a form where it can easily be unified with the electromagnetic coupling as it is commonly used in modern particle physics calculations. The Dirac equation describes antiparticles as negative-energy states. We find a symmetry of the gravitationally coupled Dirac equation, which connects particle and antiparticle solutions for a general space-time metric of the Schwarzschild type and implies that particles and antiparticles experience the same coupling to the gravitational field, including all relativistic quantum corrections of motion. Our results demonstrate the consistency of quantum mechanics with general relativity and imply that a conceivable difference of gravitational interaction of hydrogen and antihydrogen should directly be attributed to a a “fifth force” (“quintessence”).

We present a scheme to enhance the precision of parameter estimation (PPE) in noisy systems by employing dynamical decoupling pulses. An exact analytical expression for the estimation precision of an unknown parameter is obtained by using the transfer matrix and time-dependent Kraus operators. We show that the PPE in noisy systems can be preserved in the Heisenberg limit by control of the dynamical decoupling pulses. It is found that a larger number of pulses and longer reservoir correlation time can greatly protect the PPE.

The accuracy of any physical scheme used to estimate the parameter describing the strength of a single qubit Pauli channel can be quantified using standard techniques from quantum estimation theory. It is known that the optimal estimation scheme, with $m$ channel invocations, uses initial states for the systems which are pure and unentangled and provides an uncertainty of $O(1/\sqrt{m})$. This protocol is analogous to a classical repetition and averaging scheme. We consider estimation schemes where the initial states available are not pure and compare a protocol involving quantum correlated states to independent state protocols analogous to classical repetition schemes. We show, that unlike the pure state case, the quantum correlated state protocol can yield greater estimation accuracy than any independent state protocol. We show that these gains persist even when the system states are separable and, in some cases, when quantum discord is absent after channel invocation. We describe the relevance of these protocols to nuclear magnetic resonance measurements.

We have studied mixed states in the system of three qubits with the property that all their partial transposes are positive; these are called PPT states. We classify a PPT state by the ranks of the state itself and its three single partial transposes. In random numerical searches, we find entangled PPT states with a large variety of rank combinations. For ranks equal to five or higher, we find both extremal and nonextremal PPT states of nearly every rank combination, with the restriction that the square sum of the four ranks of an extremal PPT state can be at most 193. We have studied especially the rank-four entangled PPT states, which are found to have rank four for every partial transpose. These states are all extremal because of the previously known result that every PPT state of rank three or less is separable. We find two distinct classes of rank-4444 entangled PPT states, identified by a real valued quadratic expression invariant under local $\text{SL}(2,\mathbb{C})$ transformations, mathematically equivalent to Lorentz transformations. This quadratic Lorentz invariant is nonzero for one class of states (type I in our terminology) and zero for the other class (type II). The previously known states based on unextendible product bases are a nongeneric subclass of the type-I states. We present analytical constructions of states of both types, general enough to reproduce all the rank-4444 PPT states we have found numerically. We can not exclude the possibility that there exist nongeneric rank-four PPT states that we do not find in our random numerical searches.

We determine transition probabilities in two exactly solvable multistate Landau-Zener (LZ) models and discuss applications of our results to the theory of dynamic passage through a phase transition in the dissipationless quantum mechanical regime. In particular, we show that the statistics of particles in a new phase demonstrate scaling behavior. Our results also reveal a symmetry that we claim is a property of a large class of multistate LZ models, whose explicit solutions are not presently known. We support our arguments by direct numerical simulations.

This paper thoroughly elucidates the relative intensities of the probe transmission in a ladder-type electromagnetically induced transparency (EIT) system by considering the optical pumping effect. The observed EIT spectra reveal a different probe or coupling power dependence for various transmission peaks. In addition to causing quantum interference, the probe and coupling laser fields realign the population of Zeeman sublevels in the ground state through optical pumping. Analytical results indicate that the re-distribution levels, failing to contribute to the EIT peaks, either out of transition path or zero transition probability, significantly affect the transmission intensity.

The photodissociation of the monoanions of chlorophylls $a$ and $b$ in the gas phase were studied using an electrostatic storage ring. The number of neutral particles produced by the photoabsorption of the ions was measured as a function of time after irradiating the ions with a laser pulse with wavelengths in the region 410−660 nm. Fast and slow decay components were observed in the photodissociation spectra of the chlorophylls, and the lifetimes of these components increased with an increase in the wavelength of the irradiating laser pulse. It is shown that the slow decay component was due to one-photon excitation whereas the fast decay component was due to two-photon excitation. A statistical model was used to simulate the decay processes, and the simulated decay spectra were in good accordance with the experimentally determined ones. The activation energies of the decay processes of the two chlorophylls were derived using the model, and were found to be approximately 0.6 eV for both. The measured wavelength spectra were markedly different from the photoabsorption spectra of the chlorophylls in the solution phase for the $B$-band-to-$Q$-band ratio.

In the present paper, we perform the classical trajectory Monte Carlo simulation of the complex dynamics of accelerating neutral atoms with linearly or circularly polarized intense laser pulses. Our simulations involve the ion motion as well as the tunneling ionization and the scattering dynamics of valence electron in the combined Coulomb and electromagnetic fields, for both helium (He) and magnesium (Mg). We show that for He atoms, only linearly polarized lasers can effectively accelerate the atoms, while for Mg atoms, we find that both linearly and circularly polarized lasers can successively accelerate the atoms. The underlying mechanism is discussed and the subcycle dynamics of accelerating trajectories is investigated. We have compared our theoretical results with a recent experiment [Eichmann Nature (London) 461, 1261 (2009)].

We analyze a system of two-component fermions, which interact via a Feshbach resonance in the presence of a three-dimensional lattice potential. By expressing a two-channel model of the resonance in the basis of Bloch states appropriate for the lattice, we derive an eigenvalue equation for the two-particle bound states, which is nonlinear in the energy eigenvalue. Compact expressions for the interchannel matrix elements, numerical methods for the solution of the nonlinear eigenvalue problem, and a renormalization procedure to remove ultraviolet divergences are presented. From the structure of the two-body solutions we identify the relevant degrees of freedom, which describe the resonance behavior in the lowest Bloch band. These degrees of freedom, which we call dressed molecules, form an effective closed channel in a many-body model of the resonance, the Fermi resonance Hamiltonian (FRH). It is shown how the properties of the FRH can be determined numerically by solving a projected lattice two-channel model at the two-particle level. As opposed to single-channel lattice models such as the Hubbard model, the FRH is valid for general $s$-wave scattering length and resonance width. Hence, the FRH provides an accurate description of the BEC-BCS crossover for ultracold fermions on an optical lattice.

We study a quantum particle in a tilted honeycomb lattice in the tight-binding approximation. First we discuss the particle eigenstates, i.e., the stationary Wannier-Stark states. These states are proved to be extended states for the rational directions of the static field and localized states for the irrational directions. We find energy bands of the extended states and analyze the localized states. It is shown, in particular, that the localized honeycomb Wannier-Stark states are chaotic states with irregular dependence of the localization length on the static field magnitude. Second we discuss Bloch oscillations of the quantum particle. Irregular Bloch oscillations for irrational directions are observed.

We consider the angular momentum of a harmonically trapped, noninteracting Fermi gas subject to either rotation or to an artificial gauge field. The angular momentum of the gas is shown to display oscillations as a function of the particle number or chemical potential. This phenomenon is analogous to the de Haas–van Alphen oscillations of the magnetization in the solid-state context. However, key differences exist between the solid-state and ultracold atomic gases that we point out and analyze. We explore the dependence of the visibility of these oscillations on the physical parameters and propose two experimental protocols for their observation. Due to the very strong dependence of the amplitude of the oscillations on temperature, we propose their use as a sensitive thermometer for Fermi gases in the low-temperature regime.

We investigate the phase structure of two-component Bose-Einstein condensates (BECs) with repulsive intra- and interspecies interactions in the presence of respective vortex-antivortex superposition states (VAVSSs). We show that different winding numbers of the vortex and antivortex and different intra- and interspecies interaction strengths may lead to different phase configurations, such as fully separated phases, inlaid separated phases, asymmetric separated phases, and partially mixed phases, where the density profile of each component displays a petal-like (or modulated petal-like) structure. A phase diagram is given for the case of equal unit winding numbers of the vortex and antivortex in the respective components, and it is shown that the conventional criterion for phase separation of two-component BECs is not applicable for the present system due to the VAVSSs. In addition, our nonlinear stability analysis indicates that the typical phase structures of two-component BECs with VAVSSs allow them to be detected in experiments. Moreover, for the case of unequal winding numbers of the vortex and antivortex in the respective components, we find that each component in any of the possible phase structures is in a cluster state of vortices and antivortices, where the topological defects appear in the form of a singly quantized visible vortex, or a hidden vortex, or a ghost vortex, depending on the specific parameters of the system. Finally, a general relationship between the vortex-antivortex cluster state and the winding numbers of vortex and antivortex is revealed.

The three-photon Compton effect is studied. An incoming photon undergoes triple scattering off a free electron, which leads to the emission of three entangled photons. We investigate the properties of both the total cross section, assuming a low-energy cutoff for the detected photons, and the differential cross section. Particular emphasis is laid on evaluating polarization-resolved cross sections. The entanglement of the final three-photon state is analyzed.

Planck's formula for blackbody radiation was formulated subject to the assumption that the radiating body is much larger than the emitted wavelength. We demonstrate that thermal radiation exceeding Planck's law may occur in a narrow spectral range when the local radius of curvature is comparable with the wavelength of the emitted radiation. Although locally the spectral enhancement may be of several orders of magnitude, the deviation from the Stefan-Boltzmann law is less than one order of magnitude. The fluctuation-dissipation theorem needs to be employed for adequate assessment of the spectrum in this regime. Several simple examples are presented as well as experimental results demonstrating the effect. For each configuration a geometric form factor needs to be incorporated into Planck's formula in order to properly describe the emitted radiation.

This paper shows that an arbitrary Gaussian pure state can be deterministically generated in a dissipative open system that has quasilocal interactions between the subsystems and couples to the surrounding environment in a local manner. A quasilocal interaction, which means that the interaction occurs among only a few subsystems, is a crucial requirement for practical engineering of a dissipative system. The key idea is that first an auxiliary system having a local interaction with the environment is prepared and then that auxiliary system is coupled to the underlying target system via a set of two-body Hamiltonians in such a way that a desired pure state is generated. Moreover, we show that even with a simple single-mode auxiliary system, the deterministic generation of an arbitrary approximate Gaussian cluster state is possible by devising an appropriate switching scheme. We discuss in a specific example how much a dissipation-induced pure Gaussian state can be perturbed by decoherence and parameter error.

Coherent population trapping (CPT) provides a highly sensitive means for probing the energy-level structure of an atomic system. For a nitrogen-vacancy center in diamond, the CPT offers an alternative to the standard optically detected magnetic resonance method for measuring the hyperfine structure of the electronic ground states. We show that the nuclear-spin-dependent CPT measures directly the hyperfine splitting of these states due to the ${}^{14}$N nuclear spin. The CPT spectral response obtained in the presence of a strong microwave field, resonant or nearly resonant with a ground-state spin transition, maps out the dynamic Stark splitting induced by the coherent spin excitation.

We study the fault tolerance of quantum low-density parity check (LDPC) codes, such as generalized toric codes with a finite rate suggested by Tillich and Zémor [in ISIT 2009: IEEE International Symposium on Information Theory (IEEE, New York, 2009)]. We show that any family of quantum LDPC codes where each syndrome measurement involves a limited number of qubits and each qubit is involved in a limited number of measurements (as well as any similarly limited family of classical LDPC codes), in which distance scales as a positive power $\alpha$ of the number of physical qubits ($\alpha <1$ for “bad” codes), has a finite error probability threshold. We conclude that for sufficiently large quantum computers, quantum LDPC codes can offer an advantage over the toric codes.

We study a continuous set of spin-1 measurements and show that for a special family of measurements parametrized by a single variable $\theta$ the possibility of hidden-variable description depends on the rationality of $\theta /\pi$.

A key lesson of the decoherence program is that information flowing out from an open system is stored in the quantum state of the surroundings. Simultaneously, quantum measurement theory shows that the evolution of any open system when its environment is measured is nonlinear and leads to pure states conditioned on the measurement record. Here we report the discovery of a fundamental relation between measurement and entanglement which is characteristic of this scenario. It takes the form of a scaling law between the amount of entanglement in the conditional state of the system and the probabilities of the experimental outcomes obtained from measuring the state of the environment, with the latter modeled as a bosonic field linearly coupled with the system. Using the scaling, we construct the distribution of entanglement over the ensemble of experimental outcomes for standard models with one open channel and provide rigorous results on finite-time disentanglement in systems coupled to non-Markovian baths. In principle, the scaling allows the direct experimental detection and quantification of entanglement in conditional states of a large class of open systems by quantum tomography of the bath even when it consists of a single mode.