We propose an experiment to directly prove the commutation relation between bosonic annihilation and creation operators, based on the recent experimental success in single-photon subtraction and addition. We devise a single-photon interferometer to realize coherent superpositions of two sequences of photon addition and subtraction. Depending on the interference outcome, the commutation relation is directly proven or a highly nonclassical state is produced. Experimental imperfections are assessed to show that the realization of the scheme is highly feasible.

We experimentally investigate the role of localization on the adiabaticity of loading a Bose-Einstein condensate into a one-dimensional optical potential comprised of a shallow primary lattice plus one or two perturbing lattice(s) of incommensurate period. We find that even a very weak perturbation causes dramatic changes in the momentum distribution and makes adiabatic loading of the combined lattice much more difficult than for a single period lattice. We interpret our results using a band-structure model and the one-dimensional Gross-Pitaevskii equation.

We report the observation of entanglement between a single trapped atom and a single photon at remote locations. The degree of coherence of the entangled atom-photon pair is verified via appropriate local correlation measurements, after communicating the photon via an optical fiber link of 300 m length to a receiver 3.5 m apart. In addition, we measured the temporal evolution of the atomic density matrix after projecting the atom via a state measurement of the photon onto several well-defined spin states. We find that the state of the single atom dephases on a time scale of $150\mu \mathrm{s}$, which represents an important step towards long-distance quantum networking with individual neutral atoms.

We introduce a simple setup corresponding to the matter-wave analogue of impurity atoms embedded in a photonic crystal and interacting with the radiation field. Atoms in a given internal level are trapped in an optical lattice, and play the role of the impurities. Atoms in an untrapped level play the role of the radiation field. The interaction is mediated by means of lasers that couple those levels. By tuning the lasers parameters, it is possible to drive the system through different regimes, and observe phenomena such as matter-wave superradiance, non-Markovian atom emission, and the appearance of bound atomic states.

We report on the direct estimation of concurrence for mixed quantum states. The used method relies on joint measurements on two copies of an entangled state. In the experimental demonstration two polarization-entangled photon pairs emitted from spontaneous parametric down-conversion are analyzed together using a linear optics controlled phase gate. We demonstrate that the measured data, without need for further numerical processing, directly yield reliable estimates, despite experimental imperfections.

We investigate the dynamics of many-body long-range interacting systems, taking the Hamiltonian mean-field model as a case study. We show that regular trajectories, associated with invariant tori of the single-particle dynamics, prevail. The presence of such tori provides a dynamical interpretation of the emergence of long-lasting out-of-equilibrium regimes observed generically in long-range systems. This is alternative to a previous statistical mechanics approach to such phenomena which was based on a maximum entropy principle. Previously detected out-of-equilibrium phase transitions are also reinterpreted within this framework.

We demonstrate that the radial degree of freedom of strings of trapped ions in the quantum regime may be prepared and controlled accurately through the variation of the external trapping potential while at the same time its properties are measurable with high spatial and temporal resolution. This provides a new testbed giving access to static and dynamical properties of the physics of quantum-many-body systems and quantum phase transitions that are hard to simulate on classical computers. Furthermore, it allows for the creation of double well potentials with experimentally accessible tunneling rates, with applications in testing the foundations of quantum physics and precision sensing.

A fundamental limit to the sensitivity of optical interferometry is thermal noise that drives fluctuations in the positions of the surfaces of the interferometer’s mirrors, and thereby in the phase of the intracavity field. Schemes for reducing this thermally driven phase noise are presented that rely upon the coherent character of the underlying displacements and strains. Although the position of the physical surface fluctuates, the optical phase upon reflection can have reduced sensitivity to this motion. While practical implementation of such schemes for coherent compensation face certain challenges, we hope to stimulate further work on this important thermal noise problem.

We present a scheme to establish nonclassical correlations in the motion of two macroscopically separated massive particles without resorting to entanglement in their internal degrees of freedom. It is based on the dissociation of a diatomic molecule with two temporally separated Feshbach pulses generating a motional state of two counterpropagating atoms that is capable of violating a Bell inequality by means of correlated single-particle interferometry. We evaluate the influence of dispersion on the Bell correlation, showing it to be important but manageable in a proposed experimental setup. The latter employs Bose-Einstein condensation of fermionic lithium atoms, uses laser-guided atom interferometry, and seems to be within the reach of present-day technology.

Random noise can generate a unidirectional heat current across asymmetric nano-objects in the absence (or against) a temperature gradient. We present a minimal model for a molecular-level stochastic heat pump that may operate arbitrarily close to the Carnot efficiency. The model consists a fluctuating molecular unit coupled to two solids characterized by distinct phonon spectral properties. Heat pumping persists for a broad range of system and bath parameters. Furthermore, by filtering the reservoirs’ phonons the pump efficiency can approach the Carnot limit.

Anyons are particlelike excitations of strongly correlated phases of matter with fractional statistics, characterized by nontrivial changes in the wave function, generalizing Bose and Fermi statistics, when two of them are interchanged. This can be used to perform quantum computations [A. Yu. Kitaev, Ann. Phys. (N.Y.) 303, 2 (2003)]. We show how to simulate the creation and manipulation of Abelian and non-Abelian anyons in topological lattice models using trapped atoms in optical lattices. Our proposal, feasible with present technology, requires an ancilla particle which can undergo single-particle gates, be moved close to each constituent of the lattice and undergo a simple quantum gate, and be detected.

The ability to store multiple optical modes in a quantum memory allows for increased efficiency of quantum communication and computation. Here we compute the multimode capacity of a variety of quantum memory protocols based on light storage in ensembles of atoms. We find that adding a controlled inhomogeneous broadening improves this capacity significantly.

Motivated by the remarkable properties of ${\mathrm{SrCu}}_2({\mathrm{BO}}_3{)}_2$ in a magnetic field, we use perturbative continuous unitary transformations to determine the magnetization plateaux of the Shastry-Sutherland model, unveiling an unexpected sequence of plateaux progressively appearing at $2/9$, $1/6$, $1/9$, and $2/15$ upon increasing the interdimer coupling. We predict that a $1/6$ plateau should be present in ${\mathrm{SrCu}}_2({\mathrm{BO}}_3{)}_2$, even if residual interactions beyond the Shastry-Sutherland are strong enough to modify the other plateaux below $1/3$. The method is extended to calculate the magnetization profile within the plateaux, leading to a local structure around triplons that agrees with NMR results on ${\mathrm{SrCu}}_2({\mathrm{BO}}_3{)}_2$.

We present a comprehensive study of the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover in fermionic ${}^6\mathrm{Li}$ using Bragg spectroscopy. A smooth transition from molecular to atomic spectra is observed with a clear signature of pairing at and above unitarity. These spectra probe the dynamic and static structure factors of the gas and provide a direct link to two-body correlations. We have characterized these correlations and measured their density dependence across the broad Feshbach resonance at 834 G.

Polyatomic molecules are generally believed to behave more statistically as the number of vibrational modes increases. We show that even at the dissociation energy, low mode populations result in many nonstatistical quantum states. We derive a scaling relation for the number of nonstatistical states as a function of molecular size. In molecules with more than 6 atoms this model predicts that the majority of states are nonstatistical at dissociation.

We demonstrate matter-wave self-imaging resulting from atomic center-of-mass motion-based interference. We show that non-negligible atomic center-of-mass motion and an instantaneous Doppler shift can drastically change the condensate momentum distribution, resulting in a periodic collapse and the recurrence of condensate diffraction probability as a function of the stationary light-field pulsing time. The observed matter-wave self-imaging is characterized by an atomic center-of-mass motion induced population amplitude interference in the presence of the light field that simultaneously minimizes all high ($n\ge 1$) diffraction orders and maximizes the zeroth diffraction component.

The sum gate is the canonical two-mode gate for universal quantum computation based on continuous quantum variables. It represents the natural analogue to a qubit C-NOT gate. In addition, the continuous-variable gate describes a quantum nondemolition (QND) interaction between the quadrature components of two light modes. We experimentally demonstrate a QND sum gate, employing the scheme by R. Filip, P. Marek, and U. L. Andersen [Phys. Rev. A 71, 042308 (2005)], solely based on off-line squeezed states, homodyne measurements, and feedforward. The results are verified by simultaneously satisfying the criteria for QND measurements in both conjugate quadratures.

We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems [F. Verstraete and J. I. Cirac, arxiv:cond-mat/0407066] and the infinite time-evolving block decimation algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition.

We study the appearance of correlated many-body phenomena in an ensemble of atoms driven resonantly into a strongly interacting Rydberg state. The ground state of the Hamiltonian describing the driven system exhibits a second order quantum phase transition. We derive the critical theory for the quantum phase transition and show that it describes the properties of the driven Rydberg system in the saturated regime. We find that the suppression of Rydberg excitations known as blockade phenomena exhibits an algebraic scaling law with a universal exponent.

The local energy defined by $H\psi /\psi$ must be equal to the exact energy $E$ at any coordinate of an atom or molecule, as long as the $\psi$ under consideration is exact. The discrepancy from $E$ of this quantity is a stringent test of the accuracy of the calculated wave function. The $H$-square error for a normalized $\psi$, defined by ${\sigma }^2\equiv ⟨\psi |(H-E{)}^2|\psi ⟩$, is also a severe test of the accuracy. Using these quantities, we have examined the accuracy of our wave function of a helium atom calculated using the free complement method that was developed to solve the Schrödinger equation. Together with the variational upper bound, the lower bound of the exact energy calculated using a modified Temple’s formula ensured the definitely correct value of the helium fixed-nucleus ground state energy to be $\mathbf{-}\mathbf{2.903}\mathbf{724}\mathbf{377}\mathbf{034}\mathbf{119}\mathbf{598}\mathbf{311}\mathbf{159}\mathbf{245}\mathbf{194}\mathbf{4}\mathrm{a}.\mathrm{u}.$, which is correct to 32 digits.