Because the state vectors of isolated systems can be changed in entangled states by processes in other isolated systems, keeping only the density matrix fixed, it is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying only on density matrices. The density matrix is defined here by the formula giving the mean values of physical quantities, which implies the same properties as the usual definition in terms of state vectors and their probabilities. This change in the description of physical states opens up a large variety of new ways that the density matrix may transform under various symmetries, different from the unitary transformations of ordinary quantum mechanics. Such new transformation properties have been explored before, but so far only for the symmetry of time translations into the future, treated as a semigroup. Here, new transformation properties are studied for general symmetry transformations forming groups, not just semigroups. Arguments that such symmetries should act on the density matrix as in ordinary quantum mechanics are presented, but all of these arguments are found to be inconclusive.

We present a theory for the emission of fermion pairs from a superfluid Fermi gas induced by photon absorption. In solid-state physics, this type of process is called double photoemission (DPE). The spectrum of the induced two-particle current (or DPE current) provides direct insight into the correlation of condensate fermion pairs. A general formalism for two-particle current induced by DPE is developed by treating the coupling of two Fermi gases with the time-dependent perturbation theory. This formalism is used to calculate the energy distributions of the DPE current from a superfluid Fermi gas in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BCS-BEC) crossover at $T=0$. We show that the DPE current has distinct contributions of the condensed pair components and uncorrelated pair states. The angular dependence of DPE current in the BCS-BEC crossover is also calculated. The DPE current of tightly bound molecules in the BEC region is determined to be quite different from that of the weakly bound Cooper pairs.

Controlled-phase (cphase) gates can be realized with trapped neutral atoms by making use of the Rydberg blockade. Achieving the ultrahigh fidelities required for quantum computation with such Rydberg gates, however, is compromised by experimental inaccuracies in pulse amplitudes and timings, as well as by stray fields that cause fluctuations of the Rydberg levels. We report here a comparative study of analytic and numerical pulse sequences for the Rydberg cphase gate that specifically examines the robustness of the gate fidelity with respect to such experimental perturbations. Analytical pulse sequences of both simultaneous and stimulated Raman adiabatic passage (STIRAP) are found to be at best moderately robust under these perturbations. In contrast, optimal control theory is seen to allow generation of numerical pulses that are inherently robust within a predefined tolerance window. The resulting numerical pulse shapes display simple modulation patterns and can be rationalized in terms of an interference between distinct two-photon Rydberg excitation pathways. Pulses of such low complexity should be experimentally feasible, allowing gate fidelities of order 99.90–99.99% to be achievable under realistic experimental conditions.

We describe two implementations of the optimal error correction algorithm known as the maximum likelihood decoder (MLD) for the two-dimensional surface code with a noiseless syndrome extraction. First, we show how to implement MLD exactly in time $O\left(n^2\right)$, where $n$ is the number of code qubits. Our implementation uses a reduction from MLD to simulation of matchgate quantum circuits. This reduction however requires a special noise model with independent bit-flip and phase-flip errors. Secondly, we show how to implement MLD approximately for more general noise models using matrix product states (MPS). Our implementation has running time $O\left(n{\chi }^3\right)$, where $\chi$ is a parameter that controls the approximation precision. The key step of our algorithm, borrowed from the density matrix renormalization-group method, is a subroutine for contracting a tensor network on the two-dimensional grid. The subroutine uses MPS with a bond dimension $\chi$ to approximate the sequence of tensors arising in the course of contraction. We benchmark the MPS-based decoder against the standard minimum weight matching decoder observing a significant reduction of the logical error probability for $\chi \ge 4$.

We describe a method to observe the dynamics of an excited-state transition in a room-temperature atomic vapor using hyperfine quantum beats. Our experiment using cesium atoms consists of a pulsed excitation of the $D{}_2$ transition and continuous-wave driving of an excited-state transition from the $6P{}_{3/2}$ state to the $7S{}_{1/2}$ state. We observe quantum beats in the fluorescence from the $6P{}_{3/2}$ state which are modified by the driving of the excited-state transition. The Fourier spectrum of the beat signal yields evidence of Autler-Townes splitting of the $6P{}_{3/2}$, $F=5$ hyperfine level and Rabi oscillations on the excited-state transition. A detailed model provides qualitative agreement with the data, giving insight to the physical processes involved.

For the hydrogenlike ${\mathrm{Ar}}^{17+}$ ion, the $1s$ Lamb shift was absolutely determined with a $1.4\%$ accuracy based on Lyman-$\alpha$ wavelength measurements that have negligible uncertainties from nuclear size effects. The result agrees with state-of-the-art quantum electrodynamics (QED) calculations, and demonstrates the suitability of Lyman-$\alpha$ transitions in highly charged ions as x-ray energy standards, accurate at the five parts-per-million level. For the heliumlike ${\mathrm{Ar}}^{16+}$ ion the transition energy for the $1s2p{}^1{P}_1\to 1s^2{}^1{S}_0$ line was also absolutely determined on an even higher level of accuracy. Additionally, we present relative measurements of transitions in ${\mathrm{S}}^{15+},{\mathrm{S}}^{14+}$, and ${\mathrm{Fe}}^{24+}$ ions. The data for the heliumlike ${\mathrm{S}}^{14+},{\mathrm{Ar}}^{16+}$, and ${\mathrm{Fe}}^{24+}$ ions stringently confirm advanced bound-state QED predictions including screened QED terms that had recently been contested.

We propose a method for the emulation of artificial spin-orbit coupling in a system of ultracold, neutral atoms trapped in a tight-binding lattice. This scheme does not involve near-resonant laser fields, avoiding the heating processes connected to the spontaneous emission of photons. In our case, the necessary spin-dependent tunnel matrix elements are generated by a rapid, spin-dependent, periodic force, which can be described in the framework of an effective, time-averaged Hamiltonian. An additional radio-frequency coupling between the spin states leads to a mixing of the spin bands.

In ongoing experiments ultracold molecules are first created in a weakly bound level of their electronic ground-state manifold, requiring further manipulation with optical fields to transfer them in their absolute ground state. We performed a detailed theoretical analysis of the spectroscopic properties of potassium rubidium diatomic to determine efficient routes for this purpose via stimulated Raman adiabatic passage. We used state-of-the-art molecular potentials, spin-orbit coupling and transition dipole moment to perform our calculations. The dependence of spin-orbit couplings with internuclear distance are of crucial importance as the relevant transitions mainly occur in the chemical bond domain. Two main mechanisms involving a different pair of excited electronic states are modeled and compared for the various isotopologues ${}^{39}\mathrm{K}{}^{85}\mathrm{Rb}$, ${}^{39}\mathrm{K}{}^{87}\mathrm{Rb}$, ${}^{40}\mathrm{K}{}^{87}\mathrm{Rb}$, and ${}^{41}\mathrm{K}{}^{87}\mathrm{Rb}$, starting from the uppermost levels of their lowest triplet state $a^3{\Sigma }^{+}$ towards the lowest vibrational level of their ground state $X^1{\Sigma }^{+}$. The present model confirms the experimental findings. In addition, it predicts a transfer scheme which involves more efficient transitions.

We present quantum observable Markov decision processes (QOMDPs), the quantum analogs of partially observable Markov decision processes (POMDPs). In a QOMDP, an agent is acting in a world where the state is represented as a quantum state and the agent can choose a superoperator to apply. This is similar to the POMDP belief state, which is a probability distribution over world states and evolves via a stochastic matrix. We show that the existence of a policy of at least a certain value has the same complexity for QOMDPs and POMDPs in the polynomial and infinite horizon cases. However, we also prove that the existence of a policy that can reach a goal state is decidable for goal POMDPs and undecidable for goal QOMDPs.

We demonstrate control over attosecond-pulse generation and shaping by numerically optimizing the synthesis of few-cycle to subcycle driver wave forms. The optical wave-form synthesis takes place in an ultrabroad spectral band covering the ultraviolet-infrared domain. These optimized driver waves are used for ultrashort single- and double-attosecond-pulse production (with tunable separation), revealing the potentials of the light wave synthesizer device demonstrated by A. Wirth et al. [Science 334, 195 (2011)]. The robustness of the results are also analyzed with respect to attosecond-pulse propagation phenomena.

It is common knowledge that a dark soliton can be excited in an ultracold atomic gas by means of the phase imprinting method. We show that, for a superfluid fermionic mixture, the standard phase imprinting procedure applied to both components fails to create a state with symmetry properties identical to those of the dark soliton solution of the Bogoliubov–de Gennes equations. To produce a dark soliton in the BCS regime, a single component of the Fermi mixture should be phase imprinted only.

We investigate quantum beats in the arrival-time distribution of single photons from a single trapped ${{}^{40}\mathrm{Ca}}^{+}$ ion, revealing their fundamentally different physical origins in two distinct experimental situations: In a $\Lambda$-type level scheme the interference of two 854-nm absorption amplitudes suppresses and enhances the emission process of Raman-scattered 393-nm photons; in a $\mathsf{V}$-type level scheme the interference of two 393-nm emission amplitudes causes a rotation of their dipole emission pattern, resulting in a temporal modulation of the detected photons. For both cases we demonstrate coherent control over the quantum-beat phase through the phases of the atomic and photonic input states, which also allows controlled adjustment of the total photon detection efficiency.

We have investigated the ultracold interspecies scattering properties of metastable triplet He and Rb. We performed state-of-the-art ab initio calculations of the relevant interaction potential, and measured the interspecies elastic cross section for an ultracold mixture of metastable triplet ${}^4\mathrm{He}$ and ${}^{87}\mathrm{Rb}$ in a quadrupole magnetic trap at a temperature of 0.5 mK. Our combined theoretical and experimental study gives an interspecies scattering length $a_{4+87}=+{17}_{-4}^{+1}{a}_0$, which prior to this work was unknown. More general, our work shows the possibility of obtaining accurate scattering lengths using ab initio calculations for a system containing a heavy, many-electron atom, such as Rb.

As quantum computing technology improves and quantum computers with a small but nontrivial number of $N\ge 100$ qubits appear feasible in the near future the question of possible applications of small quantum computers gains importance. One frequently mentioned application is Feynman's original proposal of simulating quantum systems and, in particular, the electronic structure of molecules and materials. In this paper, we analyze the computational requirements for one of the standard algorithms to perform quantum chemistry on a quantum computer. We focus on the quantum resources required to find the ground state of a molecule twice as large as what current classical computers can solve exactly. We find that while such a problem requires about a 10-fold increase in the number of qubits over current technology, the required increase in the number of gates that can be coherently executed is many orders of magnitude larger. This suggests that for quantum computation to become useful for quantum chemistry problems, drastic algorithmic improvements will be needed.

We show that by coupling two hyperfine states of an atom in an optical lattice one can independently control two-, three-, and four-body on-site interactions in a nonperturbative manner. In particular, under typical conditions of current experiments, one can have a purely three- or four-body interacting gas of ${}^{39}\mathrm{K}$ atoms characterized by on-site interaction shifts of several 100 Hz.

We provide a comprehensive comparison of a coupled channel calculation, the asymptotic bound-state model (ABM), and the multichannel quantum defect theory (MQDT). Quantitative results for ${}^6\text{Li}-{}^{133}\text{Cs}$are presented and compared to previously measured ${}^6\text{Li}-{}^{133}\text{Cs}$Feshbach resonances (FRs) [Repp et al., Phys. Rev. A 87, 010701(R) (2013)]. We demonstrate how the accuracy of the ABM can be stepwise improved by including magnetic dipole-dipole interactions and coupling to a nondominant virtual state. We present a MQDT calculation, where magnetic dipole-dipole and second-order spin-orbit interactions are included. A frame transformation formalism is introduced, which allows the assignment of measured FRs with only three parameters. All three models achieve a total rms error of $<1\mathrm{G}$ on the observed FRs. We critically compare the different models in view of the accuracy for the description of FRs and the required input parameters for the calculations.

An allowed $E1$-$M1$ excitation scheme creates optical access to the ${}^1{S}_0\to {}^3{P}_0$ clock transition in group-II-type atoms. This method does not require the hyperfine mixing or application of an external magnetic field of other optical clock systems. The advantages of this technique include a Doppler-free excitation scheme and increased portability with the use of vapor cells. We will discuss technical mechanisms of a monochromatic excitation scheme for a hot $E1$-$M1$ clock and briefly discuss a bichromatic scheme to eliminate light shifts. We determine the optimal experimental parameters for Hg, Yb, Ra, Sr, Ba, Ca, Mg, and Be and calculate that neutral Hg has ideal properties for a hot, portable frequency standard.

A focusing Kerr Fabry-Pérot cavity operating in a negative diffraction regime exhibits transverse propagating fronts connecting two different nematic liquid crystal molecule average orientations. Under an inhomogeneous spatial pumping beam, these fronts stop to propagate and lead to the formation of a stable localized structure. The trajectory of the front position is derived from the mean-field model. Its hyperbolic tangent analytical expression perfectly fits the experimental data.

We demonstrate imaging of neutral atoms via the light scattered during continuous Raman sideband cooling. We detect single atoms trapped in optical tweezers while maintaining a significant motional ground-state fraction. The techniques presented provide a framework for single-atom resolved imaging of a broad class of atomic species.

We present a scheme for cooling mechanical motion to the ground state in an optomechanical system. Unlike standard sideband cooling, this scheme applies to the so-called unresolved sideband regime, where the resonance frequency of the mechanical mode is much smaller than the cavity linewidth. Ground-state cooling becomes possible when assuming the presence of an additional, auxiliary mechanical mode and exploiting the effect of optomechanically induced transparency. We first consider a system where one optical cavity interacts with two mechanical modes and show that ground-state cooling of the unresolved mechanical mode is possible when the auxiliary mode is in the resolved sideband regime. We then present a modified setup involving two cavity modes, where both mechanical modes are allowed to be in the unresolved sideband regime.