We demonstrate how to use feedback to control the internal states of trapped coherent ensembles of two-level atoms, and to protect a superposition state against the decoherence induced by a collective noise. Our feedback scheme is based on weak optical measurements with negligible backaction followed by coherent microwave manipulations. The efficiency of the feedback system is studied for a simple binary noise model and characterized in terms of the trade-off between information retrieval and destructivity from the optical probe. We also demonstrate the correction of more general types of collective noise. This technique can be used for the operation of atomic interferometers beyond the standard Ramsey scheme, opening the way towards improved atomic sensors.

Measurement is integral to quantum information processing and communication; it is how information encoded in the state of a system is transformed into classical signals for further use. In quantum optics, measurements are typically destructive, so that the state is not available afterwards for further steps. Here we show how to measure the presence or absence of the vacuum in a quantum optical field without destroying the state, implementing the ideal projections onto the respective subspaces. This not only enables sequential measurements, useful for quantum communication, but it can also be adapted to create novel states of light via bare raising and lowering operators.

How much information can a transmitted physical system fundamentally communicate? We introduce the principle of quantum information causality, which states the maximum amount of quantum information that a quantum system can communicate as a function of its dimension, independently of any previously shared quantum physical resources. We present a new quantum information task, whose success probability is upper bounded by the new principle, and show that an optimal strategy to perform it combines the quantum teleportation and superdense coding protocols with a task that has classical inputs.

The role of the timing and order of quantum measurements is not just a fundamental question of quantum mechanics, but also a puzzling one. Any part of a quantum system that has finished evolving can be measured immediately or saved for later, without affecting the final results, regardless of the continued evolution of the rest of the system. In addition, the nonlocality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spacelike separation, but also to particles with timelike separation. In order to demonstrate these principles, we generated and fully characterized an entangled pair of photons that have never coexisted. Using entanglement swapping between two temporally separated photon pairs, we entangle one photon from the first pair with another photon from the second pair. The first photon was detected even before the other was created. The observed two-photon state demonstrates that entanglement can be shared between timelike separated quantum systems.

We analyze a single-shot readout for superconducting qubits via the controlled catch, dispersion, and release of a microwave field. A tunable coupler is used to decouple the microwave resonator from the transmission line during the dispersive qubit-resonator interaction, thus circumventing damping from the Purcell effect. We show that, if the qubit frequency tuning is sufficiently adiabatic, a fast high-fidelity qubit readout is possible, even in the strongly nonlinear dispersive regime. Interestingly, the Jaynes-Cummings nonlinearity leads to the quadrature squeezing of the resonator field below the standard quantum limit, resulting in a significant decrease of the measurement error.

We introduce a parallel Wang-Landau method based on the replica-exchange framework for Monte Carlo simulations. To demonstrate its advantages and general applicability for simulations of complex systems, we apply it to different spin models including spin glasses, the Ising model, and the Potts model, lattice protein adsorption, and the self-assembly process in amphiphilic solutions. Without loss of accuracy, the method gives significant speed-up and potentially scales up to petaflop machines.

We present a semiclassical theoretical framework on light-wave mixing and scattering with single-component quantum gases. We show that these optical processes originating from elementary excitations with dominant collective atomic recoil motion are stimulated Raman or hyper-Raman in nature. In the forward direction the wave-mixing process, which is the most efficient process in normal gases, is strongly reduced by the condensate structure factor even though the Bogoliubov dispersion relation automatically compensates the optical-wave phase mismatch. In the backward direction, however, the free-particle-like condensate structure factor and Bogoliubov dispersion result in highly efficient light-wave mixing and collective atomic recoil motion that are enhanced by a stimulated hyper-Raman gain and a very narrow two-photon motional state resonance.

We derive reliable entanglement witnesses for coarse-grained measurements on continuous variable systems. These witnesses never return a “false positive” for identification of entanglement, under any degree of coarse graining. We show that even in the case of Gaussian states, entanglement witnesses based on the Shannon entropy can outperform those based on variances. We apply our results to experimental identification of spatial entanglement of photon pairs.

We study the behavior of the Rényi entropies for the toric code subject to a variety of different perturbations, by means of 2D density matrix renormalization group and analytical methods. We find that Rényi entropies of different index $\alpha$ display derivatives with opposite sign, as opposed to typical symmetry breaking states, and can be detected on a very small subsystem regardless of the correlation length. This phenomenon is due to the presence in the phase of a point with flat entanglement spectrum, zero correlation length, and area law for the entanglement entropy. We argue that this kind of splitting is common to all the phases with a certain group theoretic structure, including quantum double models, cluster states, and other quantum spin liquids. The fact that the size of the subsystem does not need to scale with the correlation length makes it possible for this effect to be accessed experimentally.

We describe how the couplings in an asynchronous kinetic Ising model can be inferred. We consider two cases: one in which we know both the spin history and the update times and one in which we know only the spin history. For the first case, we show that one can average over all possible choices of update times to obtain a learning rule that depends only on spin correlations and can also be derived from the equations of motion for the correlations. For the second case, the same rule can be derived within a further decoupling approximation. We study all methods numerically for fully asymmetric Sherrington-Kirkpatrick models, varying the data length, system size, temperature, and external field. Good convergence is observed in accordance with the theoretical expectations.

We study the effects of a topological Theta term on $2+1$-dimensional principal chiral models, which are nonlinear sigma models defined on Lie group manifolds. We find that when $\Theta =\pi$, the nature of the disordered phase of the principal chiral model is strongly affected by the topological term: it is either a gapless conformal field theory, or it is gapped and twofold degenerate. The result of our Letter can be used to analyze the boundary states of three-dimensional symmetry protected topological phases.

We have observed the Bose-Einstein condensation of an atomic gas in the (quasi)uniform three-dimensional potential of an optical box trap. Condensation is seen in the bimodal momentum distribution and the anisotropic time-of-flight expansion of the condensate. The critical temperature agrees with the theoretical prediction for a uniform Bose gas. The momentum distribution of a noncondensed quantum-degenerate gas is also clearly distinct from the conventional case of a harmonically trapped sample and close to the expected distribution in a uniform system. We confirm the coherence of our condensate in a matter-wave interference experiment. Our experiments open many new possibilities for fundamental studies of many-body physics.

Dephasing—phase randomization of a quantum superposition state—is a major obstacle for the realization of high fidelity quantum logic operations. Here, we implement a two-qubit controlled-NOT gate using dynamical decoupling (DD), despite the gate time being more than 1 order of magnitude longer than the intrinsic coherence time of the system. For realizing this universal conditional quantum gate, we have devised a concatenated DD sequence that ensures robustness against imperfections of DD pulses that otherwise may destroy quantum information or interfere with gate dynamics. We compare its performance with three other types of DD sequences. These experiments are carried out using a well-controlled prototype quantum system—trapped atomic ions coupled by an effective spin-spin interaction. The scheme for protecting conditional quantum gates demonstrated here is applicable to other physical systems, such as nitrogen vacancy centers, solid state nuclear magnetic resonance, and circuit quantum electrodynamics.

We propose a general framework to solve tight binding models in $D$ dimensional lattices driven by ac electric fields. Our method is valid for arbitrary driving regimes and allows us to obtain effective Hamiltonians for different external field configurations. We establish an equivalence with time-independent lattices in $D+1$ dimensions and analyze their topological properties. Furthermore, we demonstrate that nonadiabaticity drives a transition from topological invariants defined in $D+1$ to $D$ dimensions. Our results have potential applications in topological states of matter and nonadiabatic topological quantum computation, predicting novel outcomes for future experiments.

We show that a one-dimensional discrete time quantum walk can be used to implement a generalized measurement in terms of a positive operator value measure (POVM) on a single qubit. More precisely, we show that for a single qubit any set of rank 1 and rank 2 POVM elements can be generated by a properly engineered quantum walk. In such a scenario the measurement of a particle at a position $x=i$ corresponds to a measurement of a POVM element $E_i$ on a qubit. Since the idea of quantum walks originates from the von Neumann model of measurement, in which the change of the position of the pointer depends on the state of the system that is being measured, we argue that von Neumann measurements can be naturally extended to POVMs if one includes the internal evolution of the system in the model.

A virial expansion of fluid pressure in powers of the density can be used to calculate a wealth of thermodynamic information, but the $N$th virial coefficient, which multiplies the $N$th power of the density in the expansion, becomes rapidly more complicated with increasing $N$. This Letter shows that the $N$th virial coefficient can be calculated using a method that scales exponentially with $N$ in computer time and memory. This is orders of magnitude more efficient than any existing method for large $N$, and the method is simple and general. New results are presented for $N=11$ and 12 for hard spheres, and $N=9$ and 10 for soft spheres.

We study a subsystem of an isolated one-dimensional correlated metal when it is driven by a steady electric field or when it relaxes after driving. We obtain numerically exact reduced density matrix $\rho$ for subsystems which are sufficiently large to give significant eigenvalue statistics and spectra of $\log (\rho )$. We show that both for generic as well as for the integrable model, the statistics follows the universality of Gaussian unitary and orthogonal ensembles for driven and equilibrium systems, respectively. Moreover, the spectra of modestly driven subsystems are well described by the Gibbs thermal distribution with the entropy determined by the time-dependent energy only.

A search for Lorentz violation in electrodynamics was performed by measuring the resonant frequency difference between two counterpropagating directions of an optical ring cavity. Our cavity contains a dielectric element, which makes our cavity sensitive to the violation. The laser frequency is stabilized to the counterclockwise resonance of the cavity, and the transmitted light is reflected back into the cavity for resonant frequency comparison with the clockwise resonance. This double-pass configuration enables a null experiment and gives high common mode rejection of environmental disturbances. We found no evidence for odd-parity anisotropy at the level of $\delta c/c\lesssim {10}^{-14}$. Within the framework of the standard model extension, our result put more than 5 times better limits on three odd-parity parameters ${\tilde{\kappa }}_{o+}^{JK}$ and a 12 times better limit on the scalar parameter ${\tilde{\kappa }}_{\mathrm{tr}}$ compared with the previous best limits.

An asymptotic scaling theory is presented using the conceptual basis of trapping-free subspace (i.e., orthogonal subspace) to establish the generic mechanism of optimal efficiency of excitation energy transfer in light-harvesting systems. A quantum state orthogonal to the trap will exhibit noise-assisted transfer, clarifying the significance of initial preparation. For such an initial state, the efficiency is enhanced in the weak damping limit ($⟨t⟩\sim 1/\Gamma$), and suppressed in the strong damping limit ($⟨t⟩\sim \Gamma$), analogous to Kramers turnover in classical rate theory. An interpolating expression $⟨t⟩=A/\Gamma +B+C\Gamma$ quantitatively describes the trapping time over the entire range of the dissipation strength, and predicts the optimal efficiency at ${\Gamma }_{\mathrm{opt}}\sim J$ for homogenous systems. In the presence of static disorder, the scaling law of transfer time with respect to dephasing rate changes from linear to square root, suggesting a weaker dependence on the environment. The prediction of the scaling theory is verified in a symmetric dendrimer system by numerically exact quantum calculations. Though formulated in the context of excitation energy transfer, the analysis and conclusions apply in general to open quantum processes, including electron transfer, fluorescence emission, and heat conduction.

Decomposing unitaries into a sequence of elementary operations is at the core of quantum computing. Information theoretic arguments show that approximating a random unitary with precision $\epsilon$ requires $\Omega \mathbf{(}\log (1/\epsilon )\mathbf{)}$ gates. Prior to our work, the state of the art in approximating a single qubit unitary included the Solovay-Kitaev algorithm that requires $O\mathbf{(}{log}^{3+\delta }(1/\epsilon )\mathbf{)}$ gates and does not use ancillae and the phase kickback approach that requires $O\mathbf{(}{log}^2(1/\epsilon )\log \log (1/\epsilon )\mathbf{)}$ gates but uses $O\mathbf{(}{log}^2(1/\epsilon )\mathbf{)}$ ancillae. Both algorithms feature upper bounds that are far from the information theoretic lower bound. In this Letter, we report an algorithm that saturates the lower bound, and as such it guarantees asymptotic optimality. In particular, we present an algorithm for building a circuit that approximates single qubit unitaries with precision $\epsilon$ using $O\mathbf{(}\log (1/\epsilon )\mathbf{)}$ Clifford and $T$ gates and employing up to two ancillary qubits. We connect the unitary approximation problem to the problem of constructing solutions corresponding to Lagrange’s four-square theorem, and thereby develop an algorithm for computing an approximating circuit using an average of $O\mathbf{(}{log}^2(1/\epsilon )\log \log (1/\epsilon )\mathbf{)}$ operations with integers.