Reliable experimental demonstrations of violations of local realism are highly desirable for fundamental tests of quantum mechanics. One can quantify the violation witnessed by an experiment in terms of a statistical $p$ value, which can be defined as the maximum probability according to local realism of a violation at least as high as that witnessed. Thus, high violation corresponds to small $p$ value. We propose a prediction-based-ratio (PBR) analysis protocol whose $p$ values are valid even if the prepared quantum state varies arbitrarily and local realistic models can depend on previous measurement settings and outcomes. It is therefore not subject to the memory loophole [J. Barrett et al., Phys. Rev. A 66, 042111 (2002)]. If the prepared state does not vary in time, the $p$ values are asymptotically optimal. For comparison, we consider protocols derived from the number of standard deviations of violation of a Bell inequality and from martingale theory [R. Gill, e-print arXiv:quant-ph/0110137]. We find that the $p$ values of the former can be too small and are therefore not statistically valid, while those derived from the latter are suboptimal. PBR $p$ values do not require a predetermined Bell inequality and can be used to compare results from different tests of local realism independent of experimental details.

Here attention is first drawn to the importance of gaining insight into Fock's early proposal for expanding the ground-state wave function for He-like atomic ions in hyperspherical coordinates. We approach the problem via two solvable models, namely, (i) the $s$-term model put forth by Temkin [Phys. Rev. 126, 130 (1962)] and (ii) the Hookean atom model proposed by Kestner and Sinanoglu [Phys. Rev. 128, 2687 (1962)]. In both cases the local kinetic energy can be obtained explicitly in hyperspherical coordinates. Separation of variables occurs in both model wave functions, though in a different context in the two cases. Finally, a k-space formulation is proposed that should eventually result in distinctive identifying characteristics of Fock's nonanalyticities for He-like atomic ions when both electrons are close to the nucleus.

Entangled qubits can increase the capacity of quantum error-correcting codes based on stabilizer codes. In addition, by using entanglement quantum stabilizer codes can be construct from classical linear codes that do not satisfy the dual-containing constraint. We show that it is possible to construct both additive and nonadditive quantum codes using the codeword stabilized quantum code framework. Nonadditive codes may offer improved performance over the more common stabilizer codes. Like other entanglement-assisted codes, the encoding procedure acts only on the qubits on Alice's side, and only these qubits are assumed to pass through the channel. However, errors in the codeword stabilized quantum code framework give rise to effective $Z$ errors on Bob's side. We use this scheme to construct entanglement-assisted nonadditive quantum codes, in particular, $($(5,16,2;1)$)$ and $($(7,4,5;4)$)$ codes.

We present a lower bound of concurrence for arbitrary-dimensional bipartite quantum states. This lower bound may be used to improve all the known lower bounds of concurrence. Moreover, the lower bound gives rise to an operational sufficient criterion of distillability of quantum entanglement. The significance of our result is illustrated by quantitative evaluation of entanglement for entangled states that fail to be identified by the usual concurrence estimation method and by showing the distillability of mixed states that cannot be recognized by other distillability criteria.

We study dynamical error suppression from the perspective of reducing sequencing complexity, with an eye toward facilitating the development of efficient semiautonomous quantum-coherent systems. To this end, we focus on digital sequences where all interpulse time periods are integer multiples of a minimum clock period and compatibility with digital classical control circuitry is intrinsic. We use so-called Walsh functions as a unifying mathematical framework; the Walsh functions are an orthonormal set of basis functions which may be associated directly with the control propagator for a digital modulation scheme. Using this insight, we characterize the suite of resulting Walsh dynamical decoupling sequences—including both familiar and novel control sequences—and identify the number of periodic square-wave (Rademacher) functions required to generate the associated Walsh function as the key determinant of the error-suppressing features. We also show how Walsh modulation may be employed for the protection of certain nontrivial logic gates. Based on these insights, we identify Walsh modulation as a digital-efficient approach for physical-layer error suppression.

We investigate a strategy for $M$-ary discrimination of nonorthogonal phase states with error rates below the homodyne limit. This strategy uses feed forward to update a reference field and signal nulling for the state discrimination. We experimentally analyze the receiver performance using postprocessing and a Bayesian strategy to emulate the feed-forward process. This analysis shows that for a moderate system detection efficiency, it is possible to surpass the homodyne error limit for quadrature phase-shift keying signals using feed forward.

In ordinary quantum theory, any mixed state can be purified in an enlarged Hilbert space by adding an ancillary system. The purified state does not depend on the state of any extraneous system with which the mixed state is going to interact or on the physical interaction. Here, we prove that it is not possible to purify a mixed state that traverses a closed timelike curve (CTC) and is allowed to interact in a consistent way with a causality-respecting (CR) quantum system in the same manner. In other words, if a CTC quantum system with a mixed state has to undergo an arbitrary interaction with an arbitrary CR system then it has to be in a “proper” mixture, as it cannot be regarded as a subsystem of a pure entangled state. Thus, in general for arbitrary interactions between CR and CTC systems, there is no universal purification by embedding in a larger Hilbert space for mixed states with CTCs. This shows that in quantum theory with CTCs there can exist proper and improper mixtures.

Quantum key distribution (QKD) takes advantage of fundamental properties of quantum physics to allow two distant parties to share a secret key; however, QKD is hampered by a distance limitation of a few hundred kilometers on Earth. The most immediate solution for global coverage is to use a satellite, which can receive separate QKD transmissions from two or more ground stations and act as a trusted node to link these ground stations. In this article we report on a system capable of performing QKD in the high loss regime expected in an uplink to a satellite using weak coherent pulses and decoy states. Such a scenario profits from the simplicity of its receiver payload, but has so far been considered to be infeasible due to very high transmission losses (40–50 dB). The high loss is overcome by implementing an innovative photon source and advanced timing analysis. Our system handles up to 57 dB photon loss in the infinite key limit, confirming the viability of the satellite uplink scenario. We emphasize that while this system was designed with a satellite uplink in mind, it could just as easily overcome high losses on any free space QKD link.

Raman lasers are used as a spectroscopic probe of the state of atoms confined in a shallow one-dimensional (1D) vertical lattice. For sufficiently long laser pulses, resolved transitions in the bottom band of the lattice between Wannier Stark states corresponding to neighboring wells are observed. Couplings between such states are measured as a function of the lattice laser intensity and compared to theoretical predictions, from which the lattice depth can be extracted. Limits to the linewidth of these transitions are investigated. Transitions to higher bands can also be induced, as well as between transverse states for tilted Raman beams. All these features allow for a precise characterization of the trapping potential and for an efficient control of the atomic external degrees of freedom.

We study the nonequiliribium dynamics of atom-molecule Bose gases in a double-well potential. In this system, the internal atom-molecule tunneling has significant influence on the dynamics. We investigate the regularity of dynamics by studying the level statistics of the quantum system. We find that chaotic energy eigenstates arise from the competition between the interwell and the atom-molecule internal tunnelings. Furthermore, we show that the physical quantities relax to the microcanonical averages in the full-quantum dynamics when the system is chaotic. This thermalization is caused by the verification of the eigenstate thermalization hypothesis (ETH). We show numerically that the onset of ETH occurs simultaneously with that of chaos. In addition, we show that the energy eigenstates become exponentially localized states simultaneously with the onset of chaos.

We investigate the behavior of a two-level atom coupled to a one-dimensional, ultracold Fermi gas. The sudden switching on of the scattering between the two entities leads to the loss of any coherence in the initial state of the impurity and we show that the exact dynamics of this process is strongly influenced by the effect of the orthogonality catastrophe within the gas. We highlight the relationship between the Loschmidt echo and the retarded Green's function—typically used to formulate the dynamical theory of the catastrophe—and demonstrate that the effect is reflected in the impurity dynamics. We show that the expected nonexponential decay of the spectral function can be observed using Ramsey interferometry on the two-level atom and comment on finite temperature effects.

We examine collective modes, stability, and BCS pairing in a quasi-two-dimensional gas of dipolar fermions aligned by an external field. By using the (conserving) Hartree-Fock approximation, which treats direct and exchange interactions on an equal footing, we obtain the spectrum of single-particle excitations and long-wavelength collective modes (zero sound) in the normal phase. It appears that exchange interactions result in strong damping of zero sound when the tilting angle between the dipoles and the normal to the plane of confinement is below some critical value. In particular, zero sound cannot propagate if the dipoles are perpendicular to the plane of confinement. At intermediate coupling, we find unstable modes that can lead either to collapse of the system or to the formation of a density wave. The BCS transition to a superfluid phase, on the other hand, occurs at arbitrarily weak strengths of the dipole-dipole interaction, provided the tilting angle exceeds a critical value. We determine the critical temperature of the transition, taking into account many-body effects as well as virtual transitions to higher excited states in the confining potential, and discuss prospects of experimental observations.

We investigate lasing and output directionality of limaçon-shaped microdisk lasers of dimensions comparable to the emission wavelength. The far-field patterns are shown to differ between lasing modes, unlike in large cavities where lasing modes exhibit universal emission directionality determined by chaotic ray dynamics. Unidirectional emission is obtained for certain modes in the wavelength-scale cavities. It results from weak coupling of nearly isotropic high-quality resonances to anisotropic low-quality resonances, combined with chiral symmetry breaking of clockwise and counterclockwise propagating waves. The latter is described by an extended ray dynamics which includes the Goos-Hänchen shift and the Fresnel filtering. Mode hybridization and wave effects in open cavities make it possible to control the output properties of individual lasing modes in wavelength-scale lasers.

We investigate the nonponderomotive nature of ultrafast plasmonic electron acceleration in strongly decaying electromagnetic fields generated by few-cycle and single-cycle femtosecond laser pulses. We clearly identify the conditions contributing to nonponderomotive acceleration and establish fundamental scaling laws and carrier-envelope phase effects. These all-optically accelerated compact, femtosecond electron sources can be utilized in contemporary ultrafast methods.

We have used the narrow $2S_{1/2}\to 3P_{3/2}$ transition in the ultraviolet (uv) to laser cool and magneto-optically trap (MOT) ${}^6$Li atoms. Laser cooling of lithium is usually performed on the $2S_{1/2}\to 2P_{3/2}$ (D2) transition, and temperatures of $\sim$300 $\mu$K are typically achieved. The linewidth of the uv transition is seven times narrower than the D2 line, resulting in lower laser cooling temperatures. We demonstrate that a MOT operating on the uv transition reaches temperatures as low as 59 $\mu$K. Furthermore, we find that the light shift of the uv transition in an optical dipole trap at 1070 nm is small and blueshifted, facilitating efficient loading from the uv MOT. Evaporative cooling of a two spin-state mixture of ${}^6$Li in the optical trap produces a quantum degenerate Fermi gas with $3\times {10}^6$ atoms in a total cycle time of only 11 s.

We consider the effect of $\alpha$ variation on the vibrational spectrum of Sr${}_2$ in the context of a planned experiment to test the stability of $\mu \equiv m_e/m_p$ using optically trapped Sr${}_2$ molecules [Zelevinsky et al., Phys. Rev. Lett. 100, 043201 (2008); Kotochigova et al., Phys. Rev. A 79, 012504 (2009)]. We find the prospective experiment to be 3 to 4 times less sensitive to fractional variation in $\alpha$ as it is to fractional variation in $\mu$. Depending on the precision ultimately achieved by the experiment, this result may give justification for the neglect of $\alpha$ variation or, alternatively, may call for its explicit consideration in the interpretation of experimental results.

We propose a simple, general, and accurate formula for analyzing the tunneling between classical configurations of a nonplanar molecule in a gas medium, as a function of the thermodynamic parameters of the gas. We apply it to two interesting cases: (i) the shift to zero frequency of the inversion line of ammonia, upon an increase in the pressure of the gas; and (ii) the destruction of the coherent tunneling of D${}_2$S${}_2$ molecules in a He gas. In both cases, we compare our analysis with previous theoretical and experimental results.

We reanalyze the problem of radiative polarization of electrons brought into collision with a circularly polarized strong plane wave. We present an independent analytical verification of formulas for the cross section given by Ivanov et al. [Eur. Phys. J. C 36, 127 (2004)]. By choosing the exact electron's helicity as the spin quantum number we show that the self-polarization effect exists only for the moderately relativistic electrons with energy $\gamma =E/m{c}^2\lesssim 10$ and only for a non-head-on collision geometry. In these conditions polarization degree may achieve values up to $65\%$, but the effective polarization time is found to be larger than 1 s even for a high-power optical or infrared laser with intensity parameter $\xi =\left|\mathbf{E}\right|m{c}^2/E_c\hslash \omega \sim 0.1$ ($E_c=m^2{c}^3/e\hslash$). This makes such a polarization practically unrealizable. We also compare these results with the ones of some papers where the high degree of polarization was predicted for ultrarelativistic case. We argue that this apparent contradiction arises due to the different choice of the spin quantum numbers. In particular, the quantum numbers that provide the high degree of polarization represent neither helicity nor transverse polarization, which makes the use of them inconvenient in practice.

We demonstrate that an attempt to measure a nonlocal in time quantity, such as the time average $\langle A{\rangle }_T$ of a dynamical variable $A$, by separating Feynman paths into ever narrower exclusive classes traps the system in eigensubspaces of the corresponding operator $\widehat{A}$. Conversely, in a long measurement of $\langle A{\rangle }_T$ to a finite accuracy, the system explores its Hilbert space and is driven to a universal steady state in which the von Neumann ensemble average of $\widehat{A}$ coincides with $\langle A{\rangle }_T$. Both effects are conveniently analyzed in terms of singularities and critical points of the corresponding amplitude distribution and the Zeno-like behavior is shown to be a consequence of the conservation of probability.

Recently, there has been much interest in the evolution of quantum particles on closed timelike curves (CTCs). However, such models typically assume pointlike particles with only two degrees of freedom; a very questionable assumption given the relativistic setting of the problem. We show that it is possible to generalize the Deutsch model of CTCs to fields using the equivalent circuit formalism. We give examples for coherent, squeezed, and single-photon states interacting with the CTC via a beamsplitter. The model is then generalized further to account for the smooth transition to normal quantum mechanics as the CTC becomes much smaller than the size of the modes interacting on it. In this limit, we find that the system behaves like a standard quantum-mechanical feedback loop.