We investigate the quantum optical properties of Maxwell's two-dimensional fish eye lens at the single-photon and single-atom level. We show that such a system mediates effectively infinite-range dipole-dipole interactions between atomic qubits, which can be used to entangle multiple pairs of distant qubits. We find that the rate of the photon exchange between two atoms, which are detuned from the cavity resonances, is well described by a model where the photon is focused to a diffraction-limited area during absorption. We consider the effect of losses on the system and study the fidelity of the entangling operation via dipole-dipole interaction. We derive our results analytically using perturbation theory and the Born-Markov approximation and then confirm their validity by numerical simulations. We also discuss how the two-dimensional Maxwell's fish eye lens could be realized experimentally using transformational plasmon optics.

We measure the complete quantum state for six modes of the electromagnetic field produced by an optical parametric oscillator. The investigation involves the sidebands of the intense pump, signal, and idler fields generated by stimulated parametric down-conversion inside a triply resonant optical resonator. We develop a theoretical model to successfully interpret the experimental results. The model takes into account the coupling of the field modes to the phonon bath of the nonlinear crystal, clearly showing the roles of different physical effects in shaping the structure of the quantum correlations between the six optical modes.

Laser cooling of atomic motion enables a wide variety of technological and scientific explorations using cold atoms. Here we focus on the effect of laser cooling on the photons instead of on the atoms. Specifically, we show that noninteracting photons can thermalize with the atoms to a grand canonical ensemble with a nonzero chemical potential. This thermalization is accomplished via scattering of light between different optical modes, mediated by the laser-cooling process. While optically thin modes lead to traditional laser cooling of the atoms, the dynamics of multiple scattering in optically thick modes has been more challenging to describe. We find that in an appropriate set of limits, multiple scattering leads to thermalization of the light with the atomic motion in a manner that approximately conserves total photon number between the laser beams and optically thick modes. In this regime, the subsystem corresponding to the thermalized modes is describable by a grand canonical ensemble with a chemical potential nearly equal to the energy of a single laser photon. We consider realization of this regime using two-level atoms in Doppler cooling, and find physically realistic conditions for rare-earth atoms. With the addition of photon-photon interactions, this system could provide a platform for exploring many-body physics.

When quantum particles are confined into lower dimensions, an effective three-body interaction inevitably arises and may cause significant consequences. Here we study bosons in one dimension with weak two-body and three-body interactions, predict the existence of two three-body bound states when both interactions are attractive, and determine their binding energies as universal functions of the two-body and three-body scattering lengths. We also show that an infinitesimal three-body attraction induces an excited bound state only for 3, 39, or more bosons. Our findings herein have direct relevance to a broad range of quasi-one-dimensional systems realized with ultracold atoms.

Shallow trimers composed of three bosonic atoms in one-dimensional harmonic waveguides are studied in the vicinity of a Feshbach resonance. It is shown that for arbitrarily large values of the one-dimensional scattering length, an excited trimer branch exists in coexistence with the dimer and the trimer of the Lieb-Liniger model.

We solve the three-boson problem with contact two- and three-body interactions in one dimension and analytically calculate the ground and excited trimer-state energies. Then, by using the diffusion Monte Carlo technique, we calculate the binding energy of three dimers formed in a one-dimensional Bose-Bose or Fermi-Bose mixture with attractive interspecies and repulsive intraspecies interactions. Combining these results with our three-body analytics, we extract the three-dimer scattering length close to the dimer-dimer zero crossing. In both considered cases, the three-dimer interaction turns out to be repulsive. Our results constitute a concrete proposal for obtaining a one-dimensional gas with a pure three-body repulsion.

A parity-time ($\mathcal{PT}$)-symmetric system emerging from a quantum dynamics is highly desirable in order to understand the possible implications of $\mathcal{PT}$ symmetry in the next generation of quantum technologies. In this work, we address this need by proposing and studying a circuit-QED architecture that consists of two coupled resonators and two qubits (each coupled to one resonator). By means of external driving fields on the qubits, we are able to tune gains and losses in the resonators. Starting with the quantum dynamics of this system, we show the emergence of the $\mathcal{PT}$ symmetry via the selection of both driving amplitudes and frequencies. We engineer the system such that a non-number-conserving dipole-dipole interaction emerges, introducing an instability at large coupling strengths. The $\mathcal{PT}$ symmetry and its breaking, as well as the predicted instability in this circuit-QED system, can be observed in a transmission experiment.

Photons from distant astronomical sources can be used as a classical source of randomness to improve fundamental tests of quantum nonlocality, wave-particle duality, and local realism through Bell's inequality and delayed-choice quantum eraser tests inspired by Wheeler's cosmic-scale Mach-Zehnder interferometer gedanken experiment. Such sources of random numbers may also be useful for information-theoretic applications such as key distribution for quantum cryptography. Building on the design of an astronomical random number generator developed for the recent cosmic Bell experiment [Handsteiner et al. Phys. Rev. Lett. 118, 060401 (2017)], in this paper we report on the design and characterization of a device that, with 20-nanosecond latency, outputs a bit based on whether the wavelength of an incoming photon is greater than or less than $\approx 700$ nm. Using the one-meter telescope at the Jet Propulsion Laboratory Table Mountain Observatory, we generated random bits from astronomical photons in both color channels from 50 stars of varying color and magnitude, and from 12 quasars with redshifts up to $z=3.9$. With stars, we achieved bit rates of $\sim 1\times {10}^6{\mathrm{Hz}/\mathrm{m}}^2$, limited by saturation of our single-photon detectors, and with quasars of magnitudes between 12.9 and 16, we achieved rates between $\sim {10}^2$ and $2\times {10}^3\mathrm{Hz}/{\mathrm{m}}^2$. For bright quasars, the resulting bitstreams exhibit sufficiently low amounts of statistical predictability as quantified by the mutual information. In addition, a sufficiently high fraction of bits generated are of true astronomical origin in order to address both the locality and freedom-of-choice loopholes when used to set the measurement settings in a test of the Bell-CHSH inequality.

We study fingering instabilities and pattern formation at the interface of an oppositely polarized two-component Bose-Einstein condensate with strong dipole-dipole interactions in three dimensions. It is shown that the rotational symmetry is spontaneously broken by fingering instability when the dipole-dipole interactions are strengthened. Frog-shaped and mushroom-shaped patterns emerge during the dynamics due to the dipolar interactions. We also demonstrate the spontaneous density modulation and domain growth of a two-component dipolar BEC in the dynamics. Bogoliubov analyses in the two-dimensional approximation are performed, and the characteristic lengths of the domains are estimated analytically. Patterns resembling those in magnetic classical fluids are modulated when the number ratio of atoms, the trap ratio of the external potential, or tilted polarization with respect to the $z$ direction is varied.

From generation of backscatter-free transmission lines, to optical isolators, to chiral Hamiltonian dynamics, breaking time-reversal symmetry is a key tool for development of next-generation photonic devices and materials. Of particular importance is the development of time-reversal-broken devices in the low-loss regime, where they can be harnessed for quantum materials and information processors. In this work, we experimentally demonstrate the isolation of a single, time-reversal-broken running-wave mode of a moderate-finesse optical resonator. Nonplanarity of the optical path produces a round-trip geometrical (Pancharatnam) polarization rotation, breaking the inversion symmetry of the photonic modes. The residual time-reversal symmetry between forward-${\sigma }^{+}$–backward-${\sigma }^{-}$ modes is broken through an atomic Faraday rotation induced by an optically pumped ensemble of ${}^{87}\mathrm{Rb}$ atoms residing in the resonator. We observe a splitting of 6.3 linewidths between time-reversal partners and a corresponding optical isolation of ∼20.1(4) dB, with 83(1)% relative forward cavity transmission. Finally, we explore the impact of twisted resonators on T-breaking of intracavity Rydberg polaritons, a crucial ingredient of photonic materials and, specifically, topological optical matter. As a highly coherent approach to time-reversal breaking, this work will find immediate application in the creation of photonic materials and also in switchable narrow-band optical isolators.

By measuring the cyclotron frequency ratio of ${}^3\mathrm{He}^{+}$ to ${\mathrm{HD}}^{+}$ directly, with confirmation from measurements using ${\mathrm{H}}_3{}^{+}$ as an intermediary, we obtain $M\left[{}^3\mathrm{He}^{+}\right]/M\left[{\mathrm{HD}}^{+}\right]=0.998048085122\left(23\right)$ and hence the mass difference $m_p+m_d-m_h=0.00589743219\left(7\right)$ u. This result disagrees by more than four standard deviations with the value inferred from current precise literature values for the atomic masses of the proton, deuteron, and nucleus of ${}^3\mathrm{He}$.

Matter-wave sensors with cold atoms have progressed tremendously over recent decades. We report a sensitive tilt sensor based on quantum technology employing cold atoms. This quantum tiltmeter is constructed with the configuration of a Ramsey-Bordé atom interferometer, achieving an improvement of nearly three orders of magnitude for tilt measurements with a short-term sensitivity of $1.3\mu {\mathrm{rad}/\mathrm{Hz}}^{1/2}$, with resolution down to $55\mathrm{nrad}$ at an integration time of 1000 s. The deformation of the Earth's surface has been monitored in a continuous run of 31 h, showing that a quantum tiltmeter can be applied to record tilt tides and can be an valuable sensor in geophysics and various scientific facilities.

Boundaries strongly affect the behavior of quantized vortices in Bose-Einstein condensates, a phenomenon particularly evident in elongated cigar-shaped traps where vortices tend to orient along a short direction to minimize energy. Remarkably, contributions to the angular momentum of these vortices are tightly confined to the region surrounding the core, in stark contrast to untrapped condensates where all atoms contribute $\hslash$. We develop a theoretical model and use this, in combination with numerical simulations, to show that such localized vortices precess in a manner analogous to that of a classical spinning top. We experimentally verify this spinning-top behavior with our real-time imaging technique that allows for the tracking of position and orientation of vortices as they dynamically evolve. Finally, we perform an in-depth numerical investigation of our real-time expansion and imaging method, with the aim of guiding future experimental implementation as well as outlining directions for its improvement.

The softness of elastic atomic collisions, defined as the average number of collisions each atom undergoes until its energy decorrelates significantly, can have a considerable effect on the decay dynamics of atomic coherence. In this paper we combine two spectroscopic methods to measure these dynamics and obtain the collisional softness of ultracold atoms in an optical trap: Ramsey spectroscopy to measure the energy decorrelation rate and echo spectroscopy to measure the collision rate. We obtain a value of 2.5(3) for the collisional softness, in good agreement with previously reported numerical molecular-dynamics simulations. This fundamental quantity is used to determine the $s$-wave scattering lengths of different atoms but has not been directly measured. We further show that the decay dynamics of the revival amplitudes in the echo experiment has a transition in its functional decay. The transition time is related to the softness of the collisions and provides yet another way to approximate it. These conclusions are supported by Monte Carlo simulations of the full echo dynamics. The methods presented here can allow measurement of a generalized softness parameter for other two-level quantum systems with discrete spectral fluctuations.

We study, theoretically and experimentally, optical properties of different types of honeycomb photonic structures, known also as “photonic graphene.” First, we employ the two-photon polymerization method to fabricate the honeycomb structures. In the experiment, we observe a strong diffraction from a finite number of elements, thus providing a unique tool to define the exact number of scattering elements in the structure with the naked eye. Next, we study theoretically the transmission spectra of both honeycomb single layer and two-dimensional (2D) structures of parallel dielectric circular rods. When the dielectric constant of the rod materials $\varepsilon$ is increasing, we reveal that a 2D photonic graphene structure transforms into a metamaterial when the lowest $\mathrm{TE}{}_{01}$ Mie gap opens up below the lowest Bragg band gap. We also observe two Dirac points in the band structure of 2D photonic graphene at the $K$ point of the Brillouin zone and demonstrate a manifestation of Dirac lensing for the TM polarization. The performance of the Dirac lens is that the 2D photonic graphene layer converts a wave from point source into a beam with flat phase surfaces at the Dirac frequency for the TM polarization.

Optically levitated nanoparticles in vacuum are a promising model system to test physics beyond our current understanding of quantum mechanics. Such experimental tests require extreme control over the dephasing of the levitated particle's motion. If the nanoparticle carries a finite net charge, it experiences a random Coulomb force due to fluctuating electric fields. This dephasing mechanism can be fully excluded by discharging the levitated particle. Here, we present a simple and reliable technique to control the charge on an optically levitated nanoparticle in vacuum. Our method is based on the generation of charges in an electric discharge and does not require additional optics or mechanics close to the optical trap.

We study the possibility of using dark solitons in quasi-one-dimensional Bose-Einstein condensates to produce two-level systems (qubits) by exploiting the intrinsic nonlinear and coherent nature of the matter waves. We calculate the soliton spectrum and the conditions for a qubit to exist. We also compute the coupling between the phonons and the solitons and investigate the emission rate of the qubit in that case. Remarkably, the qubit lifetime is estimated to be of the order of a few seconds, being only limited by the dark-soliton “death” due to quantum evaporation.

The traveling-salesman problem is one of the most famous problems in graph theory. However, little is currently known about the extent to which quantum computers could speed up algorithms for the problem. In this paper, we prove a quadratic quantum speedup when the degree of each vertex is at most 3 by applying a quantum backtracking algorithm to a classical algorithm by Xiao and Nagamochi. We then use similar techniques to accelerate a classical algorithm for when the degree of each vertex is at most 4, before speeding up higher-degree graphs via reductions to these instances.

In this article, we experimentally demonstrate a way of controlling the group velocity of an optical pulse by using a combination of spectral hole burning, the slow-light effect, and the linear Stark effect in a rare-earth-ion–doped crystal. The group velocity can be changed continuously by a factor of 20 without significant pulse distortion or absorption of the pulse energy. With a similar technique, an optical pulse can also be compressed in time. Theoretical simulations were developed to simulate the group-velocity control and the pulse compression processes. The group velocity as well as the pulse reshaping are solely controlled by external voltages which makes it promising in quantum information and quantum communication processes. It is also proposed that the group velocity can be changed even more in an Er-doped crystal while at the same time having a transmission band matching the telecommunication wavelength.

Given a classical, reversible dynamics over a line of discrete systems, we can define a quantum evolution, which acts on basis states like the classical one but is linearly extended to allow for quantum superpositions. It is a curious fact that in the quantum regime, the speed of propagation of information can sometimes be much greater than in the classical regime. Here we provide optimal bounds on this quantum speedup. In particular we show that over a run of many steps, the quantum propagation neighborhood can only increase by a constant fringe, so that there is no asymptotic increase in speed.