Tests of the universality of free fall and the weak equivalence principle probe the foundations of general relativity. Evidence of a violation may lead to the discovery of a new force. The best torsion balance experiments have ruled it out to ${10}^{-13}$. Cold-atom drop tests have reached ${10}^{-7}$ and promise to do 7 to 10 orders of magnitude better, on the ground or in space. They are limited by the random shot noise, which depends on the number $N$ of atoms in the clouds (as $1/\sqrt{N}$). As mass-dropping experiments in the nonuniform gravitational field of Earth, they are sensitive to the initial conditions. Random accelerations due to initial condition errors of the clouds are designed to be at the same level as shot noise, so that they can be reduced with the number of drops along with it. This sets the requirements for the initial position and velocity spreads of the clouds with given $N$. In the STE-QUEST space mission proposal aiming at $2\times {10}^{-15}$ they must be about a factor 8 above the limit established by Heisenberg's uncertainty principle, and the integration time required to reduce both errors is 3 years, with a mission duration of 5 years. Instead, offset errors at release between position and velocity of different atom clouds are systematic and give rise to a systematic effect which mimics a violation. Such systematic offsets must be demonstrated to be as small as required in all drops, i.e., they must be kept small by design, and they must be measured. For STE-QUEST to meet its goal they must be several orders of magnitude smaller than the size—in position and velocity space—of each individual cloud, which in its turn must be at most 8 times larger than the uncertainty principle limit. Even if all technical problems are solved and different atom clouds are released with negligible systematic errors, still these errors must be measured; and Heisenberg's principle dictates that such measurement lasts as long as the experiment. While shot noise is random, hence its reduction becomes apparent as more and more drops are performed, the systematic effect due to offset errors at release must be identified through its specific known signature, and measured in order to be distinguished with certainty from the signal. This requires many well designed measurements to be performed—each to the target precision—for it to be ruled out as a source of violation. Ways may be pursued in order to mitigate the limitations identified here.

We study the strong coupling between photons and atoms that can be achieved in an optical nanofiber geometry when the interaction is dispersive. While the Purcell enhancement factor for spontaneous emission into the guided mode does not reach the strong-coupling regime for individual atoms, one can obtain high cooperativity for ensembles of a few thousand atoms due to the tight confinement of the guided modes and constructive interference over the entire chain of trapped atoms. We calculate the dyadic Green's function, which determines the scattering of light by atoms in the presence of the fiber, and thus the phase shift and polarization rotation induced on the guided light by the trapped atoms. The Green's function is related to a full Heisenberg-Langevin treatment of the dispersive response of the quantized field to tensor polarizable atoms. We apply our formalism to quantum nondemolition (QND) measurement of the atoms via polarimetry. We study shot-noise-limited detection of atom number for atoms in a completely mixed spin state and the squeezing of projection noise for atoms in clock states. Compared with squeezing of atomic ensembles in free space, we capitalize on unique features that arise in the nanofiber geometry including anisotropy of both the intensity and polarization of the guided modes. We use a first-principles stochastic master equation to model the squeezing as a function of time in the presence of decoherence due to optical pumping. We find a peak metrological squeezing of $\sim 5$ dB is achievable with current technology for $\sim 2500$ atoms trapped 180 nm from the surface of a nanofiber with radius $a=225$ nm.

We present the uncertainty relation for the characteristic functions (ChUR) of the quantum mechanical position and momentum probability distributions. This inequality is more general than the Heisenberg uncertainty relation and is saturated in two extreme cases for wave functions described by periodic Dirac combs. We further discuss a broad spectrum of applications of the ChUR; in particular, we constrain quantum optical measurements involving general detection apertures and provide the uncertainty relation that is relevant for loop quantum cosmology. A method to measure the characteristic function directly using an auxiliary qubit is also briefly discussed.

Various implementations of the Toffoli gate up to a relative phase have been known for years. The advantage over the regular Toffoli gate is its smaller circuit size. However, its use has been often limited to a demonstration of quantum control in designs such as those where the Toffoli gate is being applied last or otherwise for some specific reasons the relative phase does not matter. It was commonly believed that the relative-phase deviations would prevent the relative-phase Toffoli gates from being very helpful in practical large-scale designs. In this paper, we report three circuit identities that provide the means for replacing certain configurations of the multiple control Toffoli gates with their simpler relative-phase implementations, up to a selectable unitary on certain qubits, and without changing the overall functionality. We illustrate the advantage via applying those identities to the optimization of the known circuits implementing multiple control Toffoli gates, and report the reductions in the controlled-not count, $T$count, as well as the number of ancillae used. We suggest that a further study of the relative-phase Toffoli implementations and their use may yield other optimizations.

It is by now well understood that quantum dissipative processes can be harnessed and turned into a resource for quantum-information processing tasks. In this paper we demonstrate yet another way in which this is true by providing a dissipation-assisted protocol for the simulation of general Markovian dynamics. More precisely, we show how a suitable coherent coupling of a quantum system to a set of Markovian dissipating qubits allows one to enact an effective Liouvillian generator of any Lindbladian form. This effective dynamical generator arises from high-order virtual-dissipative processes and governs the system dynamics exactly in the limit of infinitely fast dissipation. Applications to the simulation of collective decoherence are discussed as an illustration.

In this paper we investigate how common the phenomenon of finite time disentanglement (FTD) is with respect to the set of quantum dynamics of bipartite quantum states with finite-dimensional Hilbert spaces. Considering a quantum dynamics from a general sense as just a continuous family of completely positive trace preserving maps (CPTP) (parametrized by the time variable) acting on the space of the bipartite systems, we conjecture that FTD happens for all dynamics but those when all maps of the family are induced by local unitary operations. We prove that this conjecture is valid for two important cases: (i) when all maps are induced by unitaries and (ii) for pairs of qubits, when all maps are unital. Moreover, we prove some general results about unitaries that preserve product states and about CPTP maps preserving pure states.

Considering ${\text{C}}_{60}$ as a model system for describing field emission from the extremity of a carbon nanotip, we explore electron emission from this fullerene excited by an intense, near-infrared, few-cycle laser pulse (${10}^{13}–{10}^{14}\text{W}/{\text{cm}}^2$, 912 nm, 8-cycle). To this end, we use time-dependent density functional theory augmented by a self-interaction correction. The ionic background of ${\text{C}}_{60}$ is described by a soft jellium model. Particular attention is paid to the high-energy electrons. Comparing the spectra at different emission angles, we find that, as a major result of this study, the photoelectrons are strongly peaked along the laser polarization axis forming a highly collimated electron beam in the forward direction, especially for the high-energy electrons. Moreover, the high-energy plateau cutoff found in the simulations agrees well with estimates from the classical three-step model. We also investigate the buildup of the high-energy part of a photoelectron spectrum by a time-resolved analysis. In particular, the modulation on the plateau can be interpreted as contributions from intracycle and intercycle interferences.

We theoretically investigate high-order-harmonic generation (HHG) in Rydberg atoms driven by spatially inhomogeneous laser fields, induced, for instance, by plasmonic enhancement. It is well known that the laser intensity should exceed a certain threshold in order to stimulate HHG when noble gas atoms in their ground state are used as an active medium. One way to enhance the coherent light coming from a conventional laser oscillator is to take advantage of the amplification obtained by the so-called surface plasmon polaritons, created when a low-intensity laser field is focused onto a metallic nanostructure. The main limitation of this scheme is the low damage threshold of the materials employed in the nanostructure engineering. In this work we propose the use of Rydberg atoms, driven by spatially inhomogeneous, plasmon-enhanced laser fields, for HHG. We exhaustively discuss the behavior and efficiency of these systems in the generation of coherent harmonic emission. Toward this aim we numerically solve the time-dependent Schrödinger equation for an atom, with an electron initially in a highly excited $n\text{th}$ Rydberg state, located in the vicinity of a metallic nanostructure. In this zone the electric field changes spatially on scales relevant for the dynamics of the laser-ionized electron. We first use a one-dimensional model to investigate systematically the phenomena. We then employ a more realistic situation, in which the interaction of a plasmon-enhanced laser field with a three-dimensional hydrogen atom is modeled. We discuss the scaling of the relevant input parameters with the principal quantum number $n$ of the Rydberg state in question and demonstrate that harmonic emission can be achieved from Rydberg atoms well below the damage threshold, thus without deterioration of the geometry and properties of the metallic nanostructure.

Coulomb explosion of 1,4–diiodobenzene molecules, isolated or embedded in helium nanodroplets, is induced by irradiation with an intense femtosecond laser pulse. The recoiling ion fragments are probed by time-of-flight measurements and two-dimensional velocity map imaging. Correlation analysis of the emission directions of ${\mathrm{I}}^{+}$ ions recoiling from each end of the molecules reveals significant deviation from axial recoil, i.e., where the ${\mathrm{I}}^{+}$ ions leave strictly along the I-I symmetry axis. For isolated molecules, the relative angular distribution of the ${\mathrm{I}}^{+}$ ions is centered at ${180}^{\circ }$, corresponding to perfect axial recoil, but with a full width at half maximum of ${30}^{\circ }$. For molecules inside He droplets, the width of the distribution increases to ${45}^{\circ }$. These results provide a direct measure of the accuracy of Coulomb explosion as a probe of the spatial orientation of molecules, which is particularly relevant in connection with laser-induced molecular alignment and orientation. In addition, our studies show how it is possible to identify fragmentation pathways of the Coulomb explosion for the isolated 1,4–diiodobenzene molecules. Finally, for the 1,4–diiodobenzene molecules in He droplets, it is shown that the angular correlation between fragments from the Coulomb explosion is preserved after they have interacted with the He environment.

Large spin systems can exhibit unconventional types of magnetic ordering, different from the ferromagnetic or Néel-like antiferromagnetic order commonly found in spin 1/2 systems. Spin-nematic phases, for instance, do not break time-reversal invariance, and their magnetic order parameter is characterized by a second-rank tensor with the symmetry of an ellipsoid. Here we show direct experimental evidence of spin-nematic ordering in a spin 1 Bose-Einstein condensate of sodium atoms with antiferromagnetic interactions. In a mean field description this order is enforced by locking the relative phase between spin components. We reveal this mechanism by studying the spin noise after a spin rotation, which is shown to contain information hidden when looking only at averages. The method should be applicable to high-spin systems in order to reveal complex magnetic phases.

The recent experimental realization of spin-orbit (SO) coupling for spin-1 ultracold atoms opens an interesting avenue for exploring SO-coupling-related physics in large-spin systems, which is generally unattainable in electronic materials. In this paper, we study the effects of interactions between atoms on the ground states and collective excitations of SO-coupled spin-1 Bose-Einstein condensates (BECs) in the presence of a spin-tensor potential. We find that ferromagnetic interaction between atoms can induce a stripe phase exhibiting in-phase or out-of-phase modulating patterns between spin-tensor and zero-spin-component density waves. We characterize the phase transitions between different phases using the spin-tensor density as well as the collective dipole motion of the BEC. We show that there exists a double maxon-roton structure in the Bogoliubov-excitation spectrum, attributed to the three band minima of the SO-coupled spin-1 BEC.

We theoretically investigate the coupling of an ultracold three-level atomic gas and a nanomechanical mirror via classical electromagnetic radiation. The radiation pressure on the mirror is modulated by absorption of a probe light field, caused by the atoms which are electromagnetically rendered nearly transparent, allowing the gas to affect the mirror. In turn, the mirror can affect the gas as its vibrations generate optomechanical sidebands in the control field. We show that the sidebands cause modulations of the probe intensity at the mirror frequency, which can be enhanced near atomic resonances. Through the radiation pressure from the probe beam onto the mirror, this results in resonant driving of the mirror. Controllable by the two-photon detuning, the phase relation of the driving to the mirror motion decides upon amplification or damping of mirror vibrations. This permits direct phase locking of laser amplitude modulations to the motion of a nanomechanical element opening a perspective for cavity-free cooling through coupling to an atomic gas.

We overcome the resolution limit of Fourier-transform spectrometry and measure instrumental line-shape-free broadband molecular spectra with lines narrower than the optical path-limited resolution. We do this by using an optical frequency comb and precisely matching the maximum delay range of the spectrometer to the comb line spacing to measure the intensities of the individual comb lines. This method allows measurements of undistorted high-resolution spectra with acquisition time and interferometer length reduced by orders of magnitude and with frequency scale accuracy given by the comb.

General properties of the Foldy-Wouthuysen transformation which is widely used in quantum mechanics and quantum chemistry are considered. Merits and demerits of the original Foldy-Wouthuysen transformation method are analyzed. While this method does not satisfy the Eriksen condition of the Foldy-Wouthuysen transformation, it can be corrected with the use of the Baker-Campbell-Hausdorff formula. We show a possibility of such a correction and propose an appropriate algorithm of calculations. An applicability of the corrected Foldy-Wouthuysen method is restricted by the condition of convergence of a series of relativistic corrections.

The Fano effect [U. Fano, Phys. Rev. 124, 1866 (1961)] shows that an inelastic scattering process can be suppressed when the output channel (OC) is coupled to an isolated bound state. The Fano effect was originally derived via a first-order perturbation treatment for coupling between the incident channel (IC) and the OC. In this paper, we first generalize the Fano effect to systems with arbitrarily strong IC-OC couplings. We analytically prove that, in a system with one IC and one OC, when the interatomic interaction potentials are real functions of the interatomic distance, the exact $s$-wave inelastic scattering amplitude can always be suppressed to zero by coupling between the IC or the OC (or both of them) and an extra isolated bound state. We further investigate the application of this generalized Fano effect for the suppression of two-body collisional losses of ultracold atoms and show that when the low-energy inelastic collision between two ultracold atoms is suppressed by this effect, the real part of the elastic scattering length between the atoms is still capable of being much larger than the range of interatomic interaction. In addition, when open scattering channels are coupled to two bound states, with the help of the Fano effect, independent control of the elastic and inelastic scattering amplitudes of two ultracold atoms can be achieved. Possible experimental realizations of our scheme are also discussed.

One-dimensional Bose gas with contact interaction in optical lattices at zero temperature is investigated by means of the exact diffusion Monte Carlo algorithm. The results obtained from the fundamental continuous model are compared with those obtained from the lattice (discrete) Bose-Hubbard model, using exact diagonalization, and from the quantum sine-Gordon model. We map out the complete phase diagram of the continuous model and determine the regions of applicability of the Bose-Hubbard model. Various physical quantities characterizing the systems are calculated, and it is demonstrated that the sine-Gordon model used for shallow lattices is inaccurate.

When light travels through strongly scattering media with optical gain, the synergy between diffusive transport and stimulated emission can lead to lasing action. Below the threshold pump power, the emission spectrum is smooth and does not change from shot to shot. Above the lasing threshold, the spectrum of emitted light becomes spiky and shows strong fluctuations from shot to shot. Recent experiments have reported that emitted intensity resembles a power-law distribution (i.e., Lévy statistics). To separate intrinsic intensity fluctuations from the motion of scatterers, we compare the statistics of samples with stationary or freely diffusing scatterers. Consistent with previous reports, we observe Lévy-like statistics when intensity data are pooled across an ensemble of scatterer configurations. For fixed scatterers, we find exponential intensity distributions for individual lasing modes whose mean intensities vary widely from mode to mode. Lévy-like statistics reemerges when data are combined across many lasing modes. Additionally, we find strong correlations of intensity fluctuations of lasing modes across wavelengths. A simple mean-field statistical model captures the observed one- and two-point statistics, where correlations in emission intensity arise from competition among all lasing modes for limited gain.

We study two-dimensional quantum mixed Gaussian packets with a fixed value of mean angular momentum. Highly mixed packets, minimizing the mean energy of an isotropic oscillator with fixed mean angular momentum $\mathcal{L}$, are found under the condition that the inverse purity ${\mathcal{P}}^{-1}$ exceeds the sum $1+2\mathcal{L}$. These states can be considered rotating thermal states. Their statistical properties (such as variances of angular momentum and energy) are studied. The case of a charged particle in a homogeneous magnetic field is considered as well.