We present an approach to monitoring and controlling a free quantum particle by coupling an internal (discrete) state of the particle to a detector (or probe). We consider a sequence of time-dependent, spatially localized interactions of the particle with the probe that are purely coherent (nondissipative), without mean energy-momentum exchange. We show that a sequence of such force-free interactions can freeze or deflect the particle.

Quantum mechanics imposes fundamental constraints known as quantum speed limits (QSLs) on the information processing speed of all quantum systems. Every QSL known to date comes from the restriction imposed on the evolution time between two quantum states through the value of a single system observable such as the mean energy relative to its ground state. So far these restrictions only place upper bounds on the information processing speed of a quantum system. Here I report QSLs each with permissible information processing speeds separated by forbidden speed intervals. They are found by a systematic and efficient procedure that takes the values of several compatible system observables into account simultaneously. This procedure generalizes almost all existing QSL proofs; the QSLs show a novel first-order phase transition in the minimum evolution time.

We introduce a fault-tolerant construction to implement a composite quantum operation of four overlapping Toffoli gates. The same construction can produce two independent Toffoli gates. This result lowers resource overheads in designs for quantum computers by more than an order of magnitude. The procedure uses Clifford operations and 64 copies of the non-Clifford gate $T=\exp [i\pi (I-{\sigma }^z)/8]$. Quantum codes detect errors in the circuit. When the dominant source of error is $T$-gate failure with probability $p$, then the composite Toffoli circuit has a postselected failure rate of $3072p^4$ to lowest order.

We investigate universal behavior in elastic atom-dimer scattering below the dimer breakup threshold calculating the atom-dimer effective-range function $ak\cot \delta$. Using the He-He system as a reference, we solve the Schrödinger equation for a family of potentials having different values of the two-body scattering length $a$ and we compare our results to the universal zero-range form deduced by Efimov, $ak\cot \delta =c_1\left(ka\right)+c_2\left(ka\right)\cot [s_0\ln \left({\kappa }_{*}a\right)+\varphi \left(ka\right)]$, for selected values of the three-body parameter ${\kappa }_{*}$. Using the parametrization of the universal functions $c_1,c_2,\varphi$ given in the literature, a good agreement with the universal formula is obtained after introducing a particular type of finite-range corrections. Furthermore, we show that the same parametrization describes a very different system: nucleon-deuteron scattering below the deuteron breakup threshold. Our analysis confirms the universal character of the process, and relates the pole energy in the effective-range function of nucleon-deuteron scattering to the three-body parameter ${\kappa }_{*}$.

Studies on ionization and electron emission from cluster nanoplasmas in intense laser fields are largely limited to experiments on single isolated clusters. We measure electron emission from ionization of clusters at higher cluster ensemble densities and find that the electron-energy spectra is highly non-Maxwellian. A comprehensive model is developed to account for the change in electron-energy spectrum and the depletion of the low-energy electron yield. It is shown that elastic and inelastic collisions account for the observed non-Maxwellian spectral shape and the computed spectrum compares well with the measurements. Furthermore, it is deciphered that the electrons that stream out of the focal volume, collisionally ionize every atom in the clusters at the periphery ($<100$ $\mu$m) of laser focus.

We demonstrate direct evaporative cooling of ${}^{87}$Rb atoms confined in a dimple trap produced by an atom chip. By changing the two chip currents and two external bias fields, we show theoretically that the trap depth can be lowered in a controlled way with no change in the trap frequencies or the value of the field at the trap center. Experimentally, we maximized the decrease in trap depth by allowing some loosening of the trap. In total, we reduced the trap depth by a factor of 20. The geometric mean of the trap frequencies was reduced by less than a factor of 6. The measured phase-space density in the final two stages increased by more than two orders of magnitude, and we estimate an increase of four orders of magnitude over the entire sequence. A subsequent rf evaporative sweep of only a few megahertz produced Bose-Einstein condensates. We also produce condensates in which raising the trap bottom pushes hotter atoms into an rf “knife” operating at a fixed frequency of 5 MHz.

We study cold rubidium Rydberg atoms, initially prepared in state $59D_{5/2}$, guided along a two-wire magnetic atom guide. The evolution of the atoms is driven by the combined effects of internal-state transitions and dipole forces acting on the center-of-mass degree of freedom. State-selective field ionization, applied at a variable delay time, is used to investigate the evolution of the internal-state distribution. We observe a broadening of the field ionization spectrum caused by population transfer between Rydberg states. At late times, the distribution of the remaining Rydberg atoms becomes biased toward states with high principal quantum numbers. The population transfer is attributed to thermal transitions and, to a lesser extent, initial state mixing due to Rydberg-Rydberg collisions. Characteristic components in spatially and temporally resolved distributions of the ion signal are interpreted in the context of the underlying physics. The system is simulated with a model in which the center-of-mass dynamics are treated classically, while the internal-state dynamics are treated quantum mechanically. The simulation qualitatively reproduces most experimental findings and provides experimentally inaccessible information.

In order to understand how stochastic processes enter and influence coherent atomic dynamics, we have studied the behavior of a Λ system under random polarization variations. Polarization, in addition to amplitude and phase, is a defining feature of a classical vector field. However, to date there has been little study of how quantum systems respond to temporal variations of polarization, even though this problem has practical implications. In our work, we generate a Bernoulli sequence of random polarization changes, and we then examine the average ${}^{87}$Rb coherent-population-trapping (CPT) line shape induced by this stochastic field. To quantitatively conceptualize our results, we have developed an independent-modulator approximation (IMA) theory for CPT line shapes induced by stochastic-polarization fields. The IMA theory is based on the idea that a power spectrum can be understood as a probability distribution of Fourier modulation frequencies. We compare the IMA theory with our experimental results, finding quite good agreement when the polarization correlation time is less than or equal to the CPT dephasing time, which is the regime of primary experimental and technological interest. The utility of the IMA theory lies in its intuitive nature, which we believe has merit for guiding experimentalists’ general understanding of stochastic fields and quantum systems.

The two-photon ladder climbing (successive two-photon Landau-Zener-type transitions) in a chirped quantum nonlinear oscillator and its classical limit (subharmonic autoresonance) are discussed. An isomorphism between the chirped one- and two-photon resonances in the system is used in calculating the threshold for the phase-locking transition in both the classical and quantum limits. The theory is tested by solving the Schrödinger equation in the energy basis and illustrated via the Wigner function in phase space.

We investigate the origin of a disagreement between the two-mode model and the exact Gross-Pitaevskii dynamics applied to double-well systems. In general this model, even in its improved version, predicts a faster dynamics and underestimates the critical population imbalance separating Josephson and self-trapping regimes. We show that the source of this mismatch in the dynamics lies in the value of the on-site interaction energy parameter. Using simplified Thomas-Fermi densities, we find that the on-site energy parameter exhibits a linear dependence on the population imbalance, which is also confirmed by Gross-Pitaevskii simulations. When introducing this dependence in the two-mode equations of motion, we obtain a reduced interaction energy parameter which depends on the dimensionality of the system. The use of this parameter significantly heals the disagreement in the dynamics and also produces better estimates of the critical imbalance.

We derive an analytical expression for the scattering amplitude of two ultracold atoms of arbitrary spin and with general spin-orbit (SO) coupling, on the basis of our recent work [Phys. Rev. A 86, 053608 (2012)]. As an application, we demonstrate that SO coupling can induce scattering resonance in the case with finite scattering length. The same approach can be applied to calculate the two-body bound state of SO-coupled ultracold atoms. For the ultracold spin-$1/2$ Fermi gases in three- or two- dimensional systems with SO coupling, we also obtain the renormalization relation of effective contact interaction with momentum cutoff, as well as the applicability of Huang-Yang pseudopotential.

We propose to realize controllable squeezing states of ferromagnetic magnons with a spinor Bose-Einstein condensate confined in an optical lattice. We use an external laser field to induce optical dipole-dipole interaction, which leads to magnon excitations of the system. By focusing on the role of the long-range magnetic and the optical dipole-dipole interactions, we show that the existence and properties of the produced squeezed magnons can be well controlled by tuning the transverse trapping widths of the condensates. We also show that the magnon excitations in this system have a close analogy with the dynamical Casimir effect at finite temperature predicted by Plunien et al. [Phys. Rev. Lett. 84, 1882 (2000)] and Jing et al. [Phys. Lett. A 268, 174 (2000)].

We describe a formulation for studying the quench dynamics of integrable systems generalizing an approach by Yudson. We study the evolution of the Lieb-Liniger model, a gas of interacting bosons moving on the continuous infinite line and interacting via a short-range potential. The formalism allows us to quench the system from any initial state. We find that for any value of repulsive coupling independently of the initial state the system asymptotes towards a strongly repulsive gas, while for any value of attractive coupling, the system forms a maximal bound state that dominates at longer times. In either case the system equilibrates but does not thermalize. We compare this to quenches in a Bose-Hubbard lattice and show that there initial states determine long-time dynamics independent of the sign of the coupling.

We consider the two-level system approximation of a single emitter driven by a continuous laser pump and simultaneously coupled to the electromagnetic vacuum and to a thermal reservoir beyond the Markovian approximation. We discuss the connection between a rigorous microscopic theory and the phenomenological spectral diffusion approach used to model the interaction of the emitter with the thermal bath. We obtain analytic expressions making it possible to deduce the thermal correlation function from the measured single-emitter photon statistics.

We demonstrate that frequency (Kerr) comb generation in whispering-gallery-mode resonators can be modeled by a variant of the Lugiato-Lefever equation that includes higher-order dispersion and nonlinearity. This spatiotemporal model allows us to explore pulse formation in which a large number of modes interact cooperatively. Pulse formation is shown to play a critical role in comb generation, and we find conditions under which single pulses (dissipative solitons) and multiple pulses (rolls) form. We show that a broadband comb is the spectral signature of a dissipative soliton, and we also show that these solitons can be obtained by using a weak anomalous dispersion and subcritical pumping.

We numerically investigate the propagation of a spatially localized and quasimonochromatic electromagnetic pulse through a slab with a Lorentz dielectric response in the epsilon-near-zero regime, where the real part of the permittivity vanishes at the pulse carrier frequency. We show that the pulse is able to excite a set of virtual polariton modes supported by the slab, with the excitation undergoing a generally slow damping due to absorption and radiation leakage. Our numerical and analytical approaches indicate that in its transient dynamics the electromagnetic field displays the very same enhancement of the field component perpendicular to the slab, as in the monochromatic regime. The transient trapping is inherently accompanied by a significantly reduced group velocity ensuing from the small dielectric permittivity, thus providing an alternative platform for achieving control and manipulation of slow light.

Two types of Hamiltonian hybrid quantum-classical theories are considered as potential models of the quantum measurement process. The two theories have the same Hamiltonian dynamics but differ in the association of states of the quantum system with states of the hybrid model. In the first type of association pure quantum states are modeled by pure states of the hybrid, while in the second type the pure quantum states are modeled by statistical mixtures of the hybrid pure states. It is shown that the second of the two theories describes correctly the quantum measurement while the first provides only an averaged description.

Collisions with chemically inert atoms or molecules change the hyperfine coupling $A\mathbf{I}·\mathbf{S}$ of an alkali-metal atom through the hyperfine-shift interaction $\delta A\mathbf{I}·\mathbf{S}$. This interaction is responsible for the pressure shifts of the microwave resonances of alkali-metal atoms in buffer gases, is an important spin interaction in alkali-metal–noble-gas van der Waals molecules, and is anticipated to enable the magnetoassociation of ultracold molecules such as RbSr. An improved estimate is presented for the long-range asymptote of this interaction for Na, K, Rb, and Cs. To test the results, the change in hyperfine coupling due to a static electric field is estimated and reasonable agreement is found.

We have successfully prepared an optically trapped ultracold mixture of ${}^{23}$Na and ${}^{87}$Rb atoms and studied their interspecies Feshbach resonances. Using two different spin combinations, several $s$- and $p$-wave resonances are identified by observing high inelastic losses and temperature increases for both species near resonant magnetic field values. The two $s$-wave resonances observed below 500 G between atoms in their lowest-energy levels are possible candidates for Feshbach molecule association. Our results are well characterized by a coupled-channel model which also refines the ground-state interaction potentials between ${}^{23}$Na and ${}^{87}$Rb. This work opens up the prospect for preparing ultracold ensembles of ground-state bosonic NaRb molecules which are chemically stable and can provide strong dipolar interactions.

The Solovay-Kitaev algorithm is the standard method used for approximating arbitrary single-qubit gates for fault-tolerant quantum computation. In this paper we introduce a technique called search space expansion, which modifies the initial stage of the Solovay-Kitaev algorithm, increasing the length of the possible approximating sequences but without requiring an exhaustive search over all possible sequences. This technique is combined with an efficient space search method called geometric nearest-neighbor access trees, modified for the unitary matrix lookup problem, in order to reduce significantly the algorithm run time. We show that, with low time cost, our techniques output gate sequences that are almost an order of magnitude smaller for the same level of accuracy. This therefore reduces the error correction requirements for quantum algorithms on encoded fault-tolerant hardware.