Some subtleties and apparent difficulties associated with the notion of spontaneous breaking of time-translation symmetry in quantum mechanics are identified and resolved. A model exhibiting that phenomenon is displayed. The possibility and significance of breaking of imaginary time-translation symmetry is discussed.

We consider the possibility that classical dynamical systems display motion in their lowest-energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary orbits of an angular variable as lowest-energy trajectories for nonsingular Lagrangian systems. Dynamics within orbits of broken symmetry provide a natural arena for formation of time crystals. We exhibit models of that kind, including a model with traveling density waves.

We introduce a new approach to evaluate transition rates for rare events in complex many-particle systems. Building on a path-integral representation of transition probabilities for Markov processes, the rate is first expressed in terms of a free energy in the transition-path ensemble. We then define an auxiliary process where a suitably defined reaction variable is dynamically decoupled from all the others, whose dynamics is left unchanged. For this system the transition rates coincide with those of a unidimensional process whose only coordinate is the reaction variable. The free-energy difference between the auxiliary and the physical transition-path ensembles is finally evaluated using standard techniques. The efficiency of this method is deemed to be optimal because the physical and auxiliary dynamics differ by one degree of freedom only at any system size. Our method is demonstrated numerically on a simple model of Lennard-Jones particles ruled by the overdamped Langevin equation.

We propose a scheme allowing us to observe the evolution of a quantum system in the semiclassical regime along the paths generated by the propagator. The scheme relies on performing consecutive weak measurements of the position. We show how “weak trajectories” can be extracted from the pointers of a series of devices having weakly interacted with the system. The properties of these weak trajectories are investigated and illustrated in the case of a time-dependent model system.

We show that the Hamiltonian of a multiband spin-orbit coupled semiconductor nanowire with Zeeman splitting and $s$-wave superconductivity is approximately chiral symmetric. The chiral symmetry becomes exact when only one pair of confinement bands is occupied and the Zeeman splitting is parallel to the nanowire. In this idealized case the Hamiltonian is in the BDI symmetry class of the topological classification of band Hamiltonians, allowing an arbitrary integer number of zero-energy Majorana fermion modes at each end. In the realistic case of multiband wires (Zeeman splitting still parallel to the length) the chiral symmetry is approximate and results in multiple near-zero-energy end states with increasing Zeeman splitting. The existence of such low energy end states implies the vanishing of the minigap with increased Zeeman splitting which can only be restored by breaking the approximate chiral symmetry by a second Zeeman field.

We perform quantum tomography on one-dimensional polariton condensates, spontaneously occurring in linear disorder valleys in a CdTe planar microcavity sample. By the use of optical interferometric techniques, we determine the first-order coherence function and the amplitude and phase of the order parameter of the condensate, providing a full reconstruction of the single particle density matrix for the polariton system. The experimental data are used as input to theoretically test the consistency of the Penrose-Onsager criterion for Bose-Einstein condensation in the framework of nonequilibrium polariton condensates. The results confirm the pertinence and validity of the criterion for a nonequilibrium condensed gas.

According to the quantum Zeno effect (QZ), frequent observations of a system can dramatically slow down its dynamical evolution. We show that the QZ is a physical consequence of the statistical indistinguishability of neighboring quantum states. The time scale of the problem is expressed in terms of the Fisher information and we demonstrate that the Zeno dynamics of particle entangled states might require quite smaller measurement intervals than classically correlated states. We propose an interferometric experiment to test the prediction.

We experimentally demonstrate polarization entanglement for squeezed vacuum pulses containing more than ${10}^5$ photons. We also study photon-number entanglement by calculating the Schmidt number and measuring its operational counterpart. Theoretically, our pulses are the more entangled the brighter they are. This promises important applications in quantum technologies, especially photonic quantum gates and quantum memories.

We derive a tight bound between the quality of estimating a quantum state by measurement and the success probability of undoing the measurement in arbitrary dimensional systems, which completely describes the tradeoff relation between the information gain and reversibility. In this formulation, it is clearly shown that the information extracted from a weak measurement is erased through the reversing process. Our result broadens the information-theoretic perspective on quantum measurement as well as provides a standard tool to characterize weak measurements and reversals.

The dynamics of the environment is usually experimentally inaccessible and hence ignored for open systems. Here we overcome this limitation by using an interferometric setup that allows the implementation of several decoherence channels and full access to all environmental degrees of freedom. We show that when a qubit from an entangled pair interacts with the environment, the initial bipartite entanglement gets redistributed into bipartite and genuine multipartite entanglements involving the two qubits and the environment. This is yet another trait of the subtle behavior of entangled open systems.

Perhaps the quantum state represents information about reality, and not reality directly. Wave function collapse is then possibly no more mysterious than a Bayesian update of a probability distribution given new data. We consider models for quantum systems with measurement outcomes determined by an underlying physical state of the system but where several quantum states are consistent with a single underlying state—i.e., probability distributions for distinct quantum states overlap. Significantly, we demonstrate by example that additional assumptions are always necessary to rule out such a model.

We discuss fluctuations near the second-order phase transition where the free energy has an additional non-Hermitian term. The spectrum of the fluctuations changes when the odd-parity potential amplitude exceeds the critical value corresponding to the $\mathcal{P}\mathcal{T}$-symmetry breakdown in the topological structure of the Hilbert space of the effective non-Hermitian Hamiltonian. We calculate the fluctuation contribution to the differential resistance of a superconducting weak link and find the manifestation of the $\mathcal{P}\mathcal{T}$-symmetry breaking in its temperature evolution. We successfully validate our theory by carrying out measurements of far from equilibrium transport in mesoscale-patterned superconducting wires.

We study rainbow (fold) and cusp catastrophes that form in Fock space following a quench in a Bose Josephson junction. In the Gross-Pitaevskii mean-field theory, the rainbows are singular caustics, but in the second-quantized theory a Poisson resummation of the wave function shows that they are described by well-behaved Airy functions. The structural stability of these Fock space caustics against variations in the initial conditions and Hamiltonian evolution is guaranteed by catastrophe theory. We also show that the long-time dynamics are ergodic. Our results are relevant to the question posed by Berry [M. V. Berry, Nonlinearity 21, T19 (2008)]: Are there circumstances when it is necessary to second quantize wave theory in order to avoid singularities?

In the setting of networked computation, data security can be a significant concern. Here we consider the problem of allowing a server to remotely manipulate client supplied data, in such a way that both the information obtained by the client about the server’s operation and the information obtained by the server about the client’s data are significantly limited. We present a protocol for achieving such functionality in two closely related models of restricted quantum computation—the boson sampling and quantum walk models. Because of the limited technological requirements of the boson scattering model, small scale implementations of this technique are feasible with present-day technology.

We report the first state-independent experimental test of quantum contextuality on a single photonic qutrit (three-dimensional system), based on a recent theoretical proposal [Phys. Rev. Lett. 108, 030402 (2012)]. Our experiment spotlights quantum contextuality in its most basic form, in a way that is independent of either the state or the tensor product structure of the system.

We solve the long-standing central spin problem for a general set of inhomogeneous bath couplings and a large class of initial bath states. We compute the time evolution of the coherence of a central spin coupled to a spin bath by resumming all orders of the time-convolutionless master equation, thus avoiding the need to assume weak coupling to the bath. The fully quantum, non-Markovian solution is obtained in the large-bath limit and is valid up to a time scale set by the largest coupling constant. Our result captures the full decoherence of an electron spin qubit coupled to a nuclear spin bath in a GaAs quantum dot for experimentally relevant parameters. In addition, our solution is quite compact and can readily be used to make quantitative predictions for the decoherence process and to guide the design of nuclear state preparation protocols.

We show that spin-orbit coupling (SOC) gives rise to pairing instability in a highly polarized two-dimensional Fermi gas for an arbitrary interaction strength. The pairing instability can lead to a Fulde-Ferrell-Larkin-Ovchinnikov-like molecular state, which undergoes a first-order transition into a pairing state with zero center-of-mass momentum as the parameters are tuned. These pairing states are metastable against a polaron state dressed by particle-hole fluctuations for small SOC. At large SOC, a polaron-molecule transition exists, which suggests a phase transition between the topological superfluid state and the normal state for a highly polarized Fermi gas in the thermodynamic limit. As polarization in a Fermi gas with SOC is induced by the effective Zeeman field, we also discuss the influences of the effective Zeeman field on the ground state of the system. Our findings may be tested directly in future experiments.

A lower bound is derived for the boundary entropy $s=\ln g$ of a ($1+1$)-dimensional quantum critical system with boundary under the conditions $c\ge 1$ on the bulk conformal central charge and ${\Delta }_1>(c-1)/12$ on the most relevant bulk scaling dimension. This is the first general restriction on the possible values of $g$ for bulk critical systems with $c\ge 1$.

The first experimental demonstration of an adaptive quantum state estimation (AQSE) is reported. The strong consistency and asymptotic efficiency of AQSE have been mathematically proven [A. Fujiwara, J. Phys. A 39, 12489 (2006)]. In this Letter, the angle of linear polarization of single photons, the phase parameter between the right and the left circularly polarization, is estimated using AQSE, and the strong consistency and asymptotic efficiency are experimentally verified. AQSE will provide a general useful method in both quantum information processing and metrology.

We develop a systematic method to extract the negativity in the ground state of a $1+1$ dimensional relativistic quantum field theory, using a path integral formalism to construct the partial transpose ${\rho }_A^{T_2}$ of the reduced density matrix of a subsystem $A=A_1\cup A_2$, and introducing a replica approach to obtain its trace norm which gives the logarithmic negativity $\mathcal{E}=\ln \Vert {\rho }_A^{T_2}\Vert$. This is shown to reproduce standard results for a pure state. We then apply this method to conformal field theories, deriving the result $\mathcal{E}\sim (c/4)\ln [{\ell }_1{\ell }_2/({\ell }_1+{\ell }_2)]$ for the case of two adjacent intervals of lengths ${\ell }_1$, ${\ell }_2$ in an infinite system, where $c$ is the central charge. For two disjoint intervals it depends only on the harmonic ratio of the four end points and so is manifestly scale invariant. We check our findings against exact numerical results in the harmonic chain.