We map the infrared dynamics of a relativistic single-component ($N=1$) interacting scalar field theory to that of nonrelativistic complex scalar fields. The Gross-Pitaevskii (GP) equation, describing the real-time dynamics of single-component ultracold Bose gases, is obtained at first nontrivial order in an expansion proportional to the powers of $\lambda {\varphi }^2/m^2$ where $\lambda$, $\varphi$, and $m$ are the coupling constant, the scalar field, and the particle mass respectively. Our analytical studies are corroborated by numerical simulations of the spatial and momentum structure of overoccupied scalar fields in (2+1)-dimensions. Universal scaling of infrared modes, vortex-antivortex superfluid dynamics, and the off-equilibrium formation of a Bose-Einstein condensate are observed. Our results for the universal scaling exponents are in agreement with those extracted in the numerical simulations of the GP equation. As in these simulations, we observe coarsening phase kinetics in the Bose superfluid with strongly anomalous scaling exponents relative to that of vertex resummed kinetic theory. Our relativistic field theory framework further allows one to study more closely the coupling between superfluid and normal fluid modes, specifically the turbulent momentum and spatial structure of the coupling between a quasiparticle cascade to the infrared and an energy cascade to the ultraviolet. We outline possible applications of the formalism to the dynamics of vortex-antivortex formation and to the off-equilibrium dynamics of the strongly interacting matter formed in heavy-ion collisions.

We study the temperature regimes of the one-dimensional interacting gas to determine when the matter wave (c-field) theory is, in fact, correct and usable. The judgment is made by investigating the level of discrepancy in many observables at once in comparison to the exact Yang-Yang theory. We also determine what cutoff maximizes the accuracy of such an approach. Results are given in terms of a bound on accuracy, as well as an optimal cutoff prescription. For a wide range of temperatures the optimal cutoff is independent of density or interaction strength and so its temperature-dependent form is suitable for many cloud shapes and, possibly, basis choices. However, this best global choice is higher in energy than most prior determinations. The high value is needed to obtain the correct kinetic energy, but does not detrimentally affect other observables.

Directional amplifiers are crucial nonreciprocal devices in both classical and quantum information processing. Here we propose a scheme for realizing a directional amplifier between optical and microwave fields based on an optomechanical system with optical gain, where an active optical cavity and two passive microwave cavities are coupled to a common mechanical resonator via radiation pressure. The two passive cavities are coupled via hopping interaction to facilitate the directional amplification between the active and passive cavities. We obtain the condition of achieving optical directional amplification and find that the direction of amplification can be controlled by the phase differences between the effective optomechanical couplings. The effects of the gain rate of the active cavity and the effective coupling strengths on the maximum gain of the amplifier are discussed. We show that the noise added to this amplifier can be greatly suppressed in the large cooperativity limit.

We propose a scheme of stabilizing the persistent-current Rabi oscillation based on the flux qubit-resonator-atom hybrid structure. The low-$Q$ $LC$ resonator weakly interacts with the flux qubit and maps the persistent-current Rabi oscillation of the flux qubit onto the intraresonator electric field. This oscillating electric field is further coupled to a Rydberg-Rydberg transition of the ${}^{87}\mathrm{Rb}$ atoms. The Rabi-frequency fluctuation of the flux qubit is deduced from measuring the atomic population via the fluorescence detection and stabilized by feedback controlling the external flux bias. Our numerical simulation indicates that the feedback-control method can efficiently suppress the background fluctuations in the flux qubit, especially in the low-frequency limit. This technique may be extensively applicable to different types of superconducting circuits, paving a way to long-term-coherence superconducting quantum information processing.

We introduce a weakening of the preparation independence postulate of Pusey et al. [Nat. Phys. 8, 475 (2012)] that does not presuppose that the space of ontic states resulting from a product-state preparation can be represented by the Cartesian product of subsystem state spaces. On the basis of this weakened assumption, it is shown that, in any model that reproduces the quantum probabilities, any pair of pure quantum states $|\psi \rangle ,|\varphi \rangle$ with $\langle \varphi |\psi \rangle \le 1/\sqrt{2}$ must be ontologically distinct.

A neutron optical experiment is presented to investigate the paths taken by neutrons in a three-beam interferometer. In various beam paths of the interferometer, the energy of the neutrons is partially shifted so that the faint traces are left along the beam path. By ascertaining an operational meaning to “the particle's path,” which-path information is extracted from these faint traces with minimal perturbations. Theory is derived by simply following the time evolution of the wave function of the neutrons, which clarifies the observation in the framework of standard quantum mechanics. Which-way information is derived from the intensity, sinusoidally oscillating in time at different frequencies, which is considered to result from the interfering cross terms between stationary main component and the energy-shifted which-way signals. Final results give experimental evidence that the (partial) wave functions of the neutrons in each beam path are superimposed and present in multiple locations in the interferometer.

The repetition code is an important primitive for the techniques of quantum error correction. Here we implement repetition codes of at most 15 qubits on the 16 qubit ibmqx3 device. Each experiment is run for a single round of syndrome measurements, achieved using the standard quantum technique of using ancilla qubits and controlled operations. The size of the final syndrome is small enough to allow for lookup table decoding using experimentally obtained data. The results show strong evidence that the logical error rate decays exponentially with code distance, as is expected and required for the development of fault-tolerant quantum computers. The results also give insight into the nature of noise in the device.

Subrotational cooling of the ${\mathrm{AlH}}^{+}$ ion to the miliKelvin regime, using optimally shaped pulses, is computed. The coherent electromagnetic fields induce purity-conserved transformations and do not change the sample temperature. A decrease in a sample temperature, manifested by an increase of purity, is achieved by the complementary uncontrolled spontaneous emission which changes the entropy of the system. We employ optimal control theory to find a pulse that stirs the system into a population configuration that will result in cooling, upon multicycle excitation-emission steps. The obtained optimal transformation was shown capable to cool molecular ions to the subkelvins regime.

We consider many-body quantum systems dissipatively coupled by a cascade network, i.e., a setup in which interactions are mediated by unidirectional environmental modes propagating through a linear optical interferometer. In particular we are interested in the possibility of inducing different effective interactions by properly engineering an external dissipative network of beam splitters and phase shifters. In this work we first derive the general structure of the master equation for a symmetric class of translation-invariant cascade networks. Then we show how, by tuning the parameters of the interferometer, one can exploit interference effects to tailor a large variety of many-body interactions.

We propose a pulsed dynamical decoupling protocol as the generator of tunable, fast, and robust quantum phase gates between two microwave-driven trapped-ion hyperfine qubits. The protocol consists of sequences of $\pi$ pulses acting on ions that are oriented along an externally applied magnetic-field gradient. In contrast to existing approaches, in our design the two vibrational modes of the ion chain cooperate under the influence of the external microwave driving to achieve significantly increased gate speeds. Our scheme is robust against the dominant noise sources, which are errors on the magnetic-field and microwave pulse intensities, as well as motional heating, predicting two-qubit gates with fidelities above 99.9% in tens of microseconds.

The natural occupation numbers of fermionic systems are subject to nontrivial constraints, which include and extend the original Pauli principle. A recent mathematical breakthrough has clarified their mathematical structure and has opened up the possibility of a systematic analysis. Early investigations have found evidence that these constraints are exactly saturated in several physically relevant systems, e.g., in a certain electronic state of the beryllium atom. It has been suggested that, in such cases, the constraints, rather than the details of the Hamiltonian, dictate the system's qualitative behavior. Here, we revisit this question with state-of-the-art numerical methods for small atoms. We find that the constraints are, in fact, not exactly saturated, but that they lie much closer to the surface defined by the constraints than the geometry of the problem would suggest. While the results seem incompatible with the statement that the generalized Pauli constraints drive the behavior of these systems, they suggest that the qualitatively correct wave-function expansions can in some systems already be obtained on the basis of a limited number of Slater determinants, which is in line with numerical evidence from quantum chemistry.

The time evolution of the trajectories, angular distributions, and two-dimensional images of intermediate-energy protons being transmitted through a conical capillary was simulated. The simulation results indicate that the charge deposited in the capillary significantly enhances the probability of surface specular scattering and thus greatly enhances the transmission rate. Furthermore, this deposited-charge-assisted specular reflection causes the transmission rate to exhibit an energy dependence proportional to $E^{-1}$, which is very consistent with the experimental data. After transmission at nonzero tilt angles, the angular distribution of several-hundred-keV protons is far from symmetric, unlike in the case of keV protons.

We consider a Bose-Einstein condensate (BEC) with attractive two-body interactions in a cigar-shaped trap, initially prepared in its ground state for a given negative scattering length, which is quenched to a larger absolute value of the scattering length. Using the mean-field approximation, we compute numerically, for an experimentally relevant range of aspect ratios and initial strengths of the coupling, two critical values of quench. One corresponds to the weakest attraction strength, the quench to which causes the system to collapse before completing even a single return from the narrow configuration (pericenter) in its breathing cycle. The other is a similar critical point for the occurrence of collapse before completing two returns. In the latter case, we also compute the limiting value, as we keep increasing the strength of the postquench attraction towards its critical value, of the time interval between the first two pericenters. We also use a Gaussian variational model to estimate the critical quenched attraction strength below which the system is stable against the collapse for long times. These time intervals and critical attraction strengths, apart from being fundamental properties of nonlinear dynamics of self-attractive BECs, may provide clues to the design of upcoming experiments that are trying to create robust BEC breathers.

We study the stability of two-domain spin structures in an ultracold gas of magnetically trapped ${}^{87}\mathrm{Rb}$ atoms above quantum degeneracy. Adding a small effective magnetic field gradient stabilizes the domains via coherent collective spin rotation effects, despite negligibly perturbing the potential energy relative to the thermal energy. We demonstrate that domain stabilization is accomplished through decoupling the dynamics of longitudinal magnetization, which remains in time-independent domains, from transverse magnetization, which undergoes a purely transverse spin wave trapped within the domain wall. We explore the effect of temperature and density on the steady-state domains, and compare our results to a hydrodynamic solution to a quantum Boltzmann equation.

We investigate the experimental setup proposed in New J. Phys. 15, 115006 (2013) for calorimetric measurements of thermodynamic indicators in an open quantum system. As a theoretical model we consider a periodically driven qubit coupled with a large yet finite electron reservoir, the calorimeter. The calorimeter is initially at equilibrium with an infinite phonon bath. As time elapses, the temperature of the calorimeter varies in consequence of energy exchanges with the qubit and the phonon bath. We show how under weak-coupling assumptions, the evolution of the qubit-calorimeter system can be described by a generalized quantum jump process including as dynamical variable the temperature of the calorimeter. We study the jump process by numeric and analytic methods. Asymptotically with the duration of the drive, the qubit-calorimeter attains a steady state. In this same limit, we use multiscale perturbation theory to derive a Fokker-Planck equation governing the calorimeter temperature distribution. We inquire the properties of the temperature probability distribution close and at the steady state. In particular, we predict the behavior of measurable statistical indicators versus the qubit-calorimeter coupling constant.

In 1961, Landauer [R. Landauer, IBM J. Res. Develop. 5, 183 (1961)] pointed out that resetting a binary memory requires a minimum energy of $k_{B}Tln\left(2\right)$. However, once written, any memory is doomed to lose its content if no action is taken. To avoid memory losses, a refresh procedure is periodically performed. We present a theoretical model and an experiment on a microelectromechanical system to evaluate the minimum energy required to preserve one bit of information over time. Two main conclusions are drawn: (i) in principle, the energetic cost to preserve information for a fixed time duration with a given error probability can be arbitrarily reduced if the refresh procedure is performed often enough, and (ii) the Heisenberg uncertainty principle sets an upper bound on the memory lifetime.

In Shor's algorithm quantum subroutines occur with the structure $\mathcal{F}\mathcal{U}{\mathcal{F}}^{-1}$, where $\mathcal{F}$ is a unitary transform and $\mathcal{U}$ is performing a quantum computation. Examples are quantum adders and subunits of quantum modulo adders. In this paper we show, both analytically and numerically, that if, in analogy to spin echoes, $\mathcal{F}$ and ${\mathcal{F}}^{-1}$ can be implemented symmetrically when executing Shor's algorithm on actual, imperfect quantum hardware, such that $\mathcal{F}$ and ${\mathcal{F}}^{-1}$ have the same hardware errors, a symmetry boost in the fidelity of the combined $\mathcal{F}\mathcal{U}{\mathcal{F}}^{-1}$ quantum operation results when compared to the case in which the errors in $\mathcal{F}$ and ${\mathcal{F}}^{-1}$ are independently random. Running the complete gate-by-gate implemented Shor algorithm, we show that the symmetry-induced fidelity boost can be as large as a factor 4. While most of our analytical and numerical results concern the case of over- and under-rotation of controlled rotation gates, in the numerically accessible case of Shor's algorithm with a small number of qubits, we show explicitly that the symmetry boost is robust with respect to more general types of errors. While, expectedly, additional error types reduce the symmetry boost, we show explicitly, by implementing general off-diagonal $\mathrm{SU}\left(N\right)$ errors ($N=2,4,8$), that the boost factor scales like a Lorentzian in $\delta /\sigma$, where $\sigma$ and $\delta$ are the error strengths of the diagonal over- and underrotation errors and the off-diagonal $\mathrm{SU}\left(N\right)$ errors, respectively. The Lorentzian shape also shows that, while the boost factor may become small with increasing $\delta$, it declines slowly (essentially like a power law) and is never completely erased. We also investigate the effect of diagonal nonunitary errors, which, in analogy to unitary errors, reduce but never erase the symmetry boost. Going beyond the case of small quantum processors, we present analytical scaling results that show that the symmetry boost persists in the practically interesting case of a large number of qubits. We illustrate this result explicitly for the case of Shor factoring of the semiprime RSA-1024, where, analytically, focusing on over- and underrotation errors, we obtain a boost factor of about 10. In addition, we provide a proof of the fidelity product formula, including its range of applicability.