We present an experimental realization of Hardy’s thought experiment [Phys. Rev. Lett. 68, 2981 (1992)], using photons. The experiment consists of a pair of Mach-Zehnder interferometers that interact through photon bunching at a beam splitter. A striking contradiction is created between the predictions of quantum mechanics and local hidden variables. The contradiction relies on nonmaximally entangled position states of two particles. A Clauser-Horne–type inequality is derived and violated.

We present a new procedure for quantum state reconstruction based on weak continuous measurement of an ensemble average. By applying controlled evolution to the initial state, new information is continually mapped onto the measured observable. A Bayesian filter is then used to update the state estimate in accordance with the measurement record. This generalizes the standard paradigm for quantum tomography based on strong, destructive measurements on separate ensembles. This approach to state estimation induces minimal perturbation of the measured system, giving information about observables whose evolution cannot be described classically in real time and opening the door to new types of quantum feedback control.

Cluster states are a new type of multiqubit entangled states with entanglement properties exceptionally well suited for quantum computation. In the present work, we experimentally demonstrate that correlations in a four-qubit linear cluster state cannot be described by local realism. This exploration is based on a recently derived Bell-type inequality [V. Scarani et al., Phys. Rev. A 71, 042325 (2005)] which is tailored, by using a combination of three- and four-particle correlations, to be maximally violated by cluster states but not violated at all by GHZ states. We observe a cluster-state Bell parameter of $2.59\pm 0.08$, which is more than $7\sigma$ larger than the threshold of 2 imposed by local realism.

We have used optical molecular spectroscopy to probe the many-body state of paired ${}^6\mathrm{L}\mathrm{i}$ atoms near a broad Feshbach resonance. The optical probe projects pairs of atoms onto a vibrational level of an excited molecule. The rate of excitation enables a precise measurement of the closed-channel contribution to the paired state. This contribution is found to be quite small, supporting the concept of universality for the description of broad Feshbach resonances. The dynamics of the excitation provide clear evidence for pairing across the BEC-BCS crossover and into the weakly interacting BCS regime.

This Letter presents a two-dimensional nuclear magnetic resonance (NMR) approach for constructing a two-logical-qubit decoherence-free subspace (DFS) by using four multiple-quantum coherences of a ${\mathrm{CH}}_3$ spin system as logical qubits. The three protons in this spin system are magnetically equivalent and can only be used as a single qubit in one-dimensional NMR. We have experimentally demonstrated that our DFS can protect against more types of decoherences than those of the one composed of four noisy physical qubits all with different chemical shifts. This idea may provide new insights into extending qubit systems in the sense that it effectively utilizes the magnetically equivalent nuclei.

We analyze the stability of superfluid currents in a system of strongly interacting ultracold atoms in an optical lattice. We show that such a system undergoes a dynamic, irreversible phase transition at a critical phase gradient that depends on the interaction strength between atoms. At commensurate filling, the phase boundary continuously interpolates between the classical modulation instability of a weakly interacting condensate and the equilibrium quantum phase transition into a Mott insulator state at which the critical current vanishes. We argue that quantum fluctuations smear the transition boundary in low dimensional systems. Finally we discuss the implications to realistic experiments.

We propose to observe Anderson localization of ultracold atoms in the presence of a random potential made of atoms of another species or spin state and trapped at the nodes of an optical lattice, with a filling factor less than unity. Such systems enable a nearly perfect experimental control of the disorder, while the possibility of modeling the scattering potentials by a set of pointlike ones allows an exact theoretical analysis. This is illustrated by a detailed analysis of the one-dimensional case.

We investigate some static and dynamic properties of harmonically trapped fermionic Tonks-Girardeau gases in tight de Broglie waveguides with attractive $p$-wave interactions induced by a Feshbach resonance. An exact solution for the one-body density matrix is analyzed in terms of its natural orbitals, with the surprising result that for odd, but not for even, numbers of fermions the maximally occupied orbital coincides with the ground harmonic oscillator orbital. A dynamical consequence of this is that when the interactions are turned off the on-axis density remains a maximum for an odd number of fermions, whereas a minimum develops for an even number.

A debated issue in the physics of the BCS-BEC crossover with trapped Fermi atoms is to identify characteristic properties of the superfluid phase. Recently, a condensate fraction was measured on the BCS side of the crossover by sweeping the system in a fast (nonadiabatic) way from the BCS to the Bose-Einstein condensation (BEC) sides, thus “projecting” the initial many-body state onto a molecular condensate. We analyze here the theoretical implications of these projection experiments, by identifying the appropriate quantum-mechanical operator associated with the measured quantities and relating them to the many-body correlations occurring in the BCS-BEC crossover. Calculations are presented over wide temperature and coupling ranges, by including pairing fluctuations on top of the mean field.

The two-loop radiative photonic corrections to Bhabha scattering are computed in the leading order of the small electron mass expansion up to the nonlogarithmic term. After including the soft photon bremsstrahlung, we obtain the infrared-finite result for the differential cross section, which can directly be applied to a precise luminosity determination of the present and future $e^{+}{e}^{-}$ colliders.

The Röntgen quantum phase shift is exhibited by the interference of point particles endowed with an electric dipole moment due to their motion relative to a source of the magnetic field. Here we show, using arguments involving the classical concepts of force and its impulse, that the Röntgen phase shift arises within a largely classical (semiclassical) theoretical framework. All the subtleties normally associated with the nonlocality of magnetic (Aharonov-Bohm-type) quantum phase phenomena are uncontroversially absent in the classical treatment.

We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with $k$ internal states, and laser assisted state sensitive tunneling, described by unitary $k\times k$ matrices. The single-particle dynamics in the case of intense $U(2)$ vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex mothlike structure. We discuss the possibility to realize non-Abelian interferometry (Aharonov-Bohm effect) and to study many-body dynamics of ultracold matter in external lattice gauge fields.

We show that the adiabatic motion of ultracold, multilevel atoms in spatially varying laser fields can give rise to effective non-Abelian gauge fields if degenerate adiabatic eigenstates of the atom-laser interaction exist. A pair of such degenerate dark states emerges, e.g., if laser fields couple three internal states of an atom to a fourth common one under pairwise two-photon-resonance conditions. For this so-called tripod scheme we derive general conditions for truly non-Abelian gauge potentials and discuss special examples. In particular we show that using orthogonal laser beams with orbital angular momentum an effective magnetic field can be generated that has a monopole component.

Fully frustrated Josephson-junction arrays (FF-JJA’s) exhibit a subtle compound phase transition in which an Ising transition associated with discrete broken translational symmetry and a Berezinskii-Kosterlitz-Thouless transition associated with quasi-long-range phase coherence occur nearly simultaneously. In this Letter we discuss a cold-atom realization of the FF-JJA system. We demonstrate that both orders can be studied by standard momentum-distribution-function measurements and present numerical results, based on a successful self-consistent spin-wave approximation, that illustrate the expected behavior of observables.

We report on the first realization of a single bosonic Josephson junction, implemented by two weakly linked Bose-Einstein condensates in a double-well potential. In order to fully investigate the nonlinear tunneling dynamics we measure the density distribution in situ and deduce the evolution of the relative phase between the two condensates from interference fringes. Our results verify the predicted nonlinear generalization of tunneling oscillations in superconducting and superfluid Josephson junctions. Additionally, we confirm a novel nonlinear effect known as macroscopic quantum self-trapping, which leads to the inhibition of large amplitude tunneling oscillations.

We introduce a scheme for linear optics quantum computation, that makes no use of teleported gates, and requires stable interferometry over only the coherence length of the photons. We achieve a much greater degree of efficiency and a simpler implementation than previous proposals. We follow the “cluster state” measurement based quantum computational approach, and show how cluster states may be efficiently generated from pairs of maximally polarization entangled photons using linear optical elements. We demonstrate the universality and usefulness of generic parity measurements, as well as introducing the use of redundant encoding of qubits to enable utilization of destructive measurements—both features of use in a more general context.

We discuss certain relations between cloning and the not operation that can be derived from conservation laws alone. Those relations link the limitations on cloning and the not operation possibly imposed by other laws of nature. Our result is quite general and holds both in classical and quantum-mechanical worlds, for both optimal and suboptimal operations, and for bosons as well as fermions.

Standard quantum key distribution protocols are provably secure against eavesdropping attacks, if quantum theory is correct. It is theoretically interesting to know if we need to assume the validity of quantum theory to prove the security of quantum key distribution, or whether its security can be based on other physical principles. The question would also be of practical interest if quantum mechanics were ever to fail in some regime, because a scientifically and technologically advanced eavesdropper could perhaps use postquantum physics to extract information from quantum communications without necessarily causing the quantum state disturbances on which existing security proofs rely. Here we describe a key distribution scheme provably secure against general attacks by a postquantum eavesdropper limited only by the impossibility of superluminal signaling. Its security stems from violation of a Bell inequality.

We present a simple quantum circuit that allows for the universal and deterministic manipulation of the quantum state of confined harmonic oscillators. The scheme is based on the selective interactions of the referred oscillator with an auxiliary three-level system and a classical external driving source, and enables any unitary operations on Fock states, two by two. One circuit is equivalent to a single qubit unitary logical gate on Fock states qubits. Sequences of similar protocols allow for complete, deterministic, and state-independent manipulation of the harmonic oscillator quantum state.

We present a general approach for computing the dynamic partition function of a continuous-time Markov process. The Ruelle topological pressure is identified with the large deviation function of a physical observable. We construct for the first time a corresponding finite Kolmogorov-Sinai entropy for these processes. Then, as an example, the latter is computed for a symmetric exclusion process. We further present the first exact calculation of the topological pressure for an $N$-body stochastic interacting system, namely, an infinite-range Ising model endowed with spin-flip dynamics. Expressions for the Kolmogorov-Sinai and the topological entropies follow.