arXiv subjects

Helmut Ritsch

Publications and source records attributed to Helmut Ritsch.

At least 55 records · Page 3Linked to original sources

arXiv2021

Cavity QED with Quantum Gases: New Paradigms in Many-Body Physics

We review the recent developments and the current status in the field of quantum-gas cavity QED. Since the first experimental demonstration of atomic self-ordering in a system composed of a Bose-Einstein condensate coupled to a quantized electromagnetic mode of a high-$Q$ optical cavity, the field has rapidly evolved over the past decade. The composite quantum-gas--cavity systems offer the opportunity to implement, simulate, and experimentally test fundamental solid-state Hamiltonians, as well as to realize non-equilibrium many-body phenomena beyond conventional condensed-matter scenarios. This hinges on the unique possibility to design and control in open quantum environments photon-induced tunable-range interaction potentials for the atoms using tailored pump lasers and dynamic cavity fields. Notable examples range from Hubbard-like models with long-range interactions exhibiting a lattice-supersolid phase, over emergent magnetic orderings and quasicrystalline symmetries, to the appearance of dynamic gauge potentials and non-equilibrium topological phases. Experiments have managed to load spin-polarized as well as spinful quantum gases into various cavity geometries and engineer versatile tunable-range atomic interactions. This led to the experimental observation of spontaneous discrete and continuous symmetry breaking with the appearance of soft-modes as well as supersolidity, density and spin self-ordering, dynamic spin-orbit coupling, and non-equilibrium dynamical self-ordered phases among others. In addition, quantum-gas--cavity setups offer new platforms for quantum-enhanced measurements. In this review, starting from an introduction to basic models, we pedagogically summarize a broad range of theoretical developments and put them in perspective with the current and near future state-of-art experiments.

cond-mat.quant-gas↗

arXiv2021

Unraveling the origin of higher success probabilities in quantum versus semi-classical annealing

Quantum annealing aims at finding optimal solutions to complex optimization problems using a suitable quantum many body Hamiltonian encoding the solution in its ground state. To find the solution one typically evolves the ground state of a soluble initial Hamiltonian adiabatically to the ground state of the designated final Hamiltonian. Here we explore whether and when a full quantum representation of the dynamics leads to higher probability to end up in the desired ground when compared to a classical mean field approximation. As simple, nontrivial example we target the ground state of interacting bosons trapped in a tight binding lattice with small local defect by turning on long range interactions. Already two atoms in four sites interacting via two cavity modes prove complex enough to exhibit significant differences between the full quantum model and a mean field approximation for the cavity fields mediating the interactions. We find a large parameter region of highly successful quantum annealing where the semi-classical approach largely fails. Here we see strong evidence for the importance of entanglement to end close to the optimal solution. The quantum model also reduces the minimal time for a high target occupation probability. In contrast to naive expectations that enlarging the Hilbert space is beneficial, different numerical cut-offs of the Hilbert space reveal an improved performance for lower cut-offs, i.e. an nonphysical reduced Hilbert space, for short simulation times. Hence a less faithful representation of the full quantum dynamics sometimes creates a higher numerical success probability in shorter time. However, a sufficiently high cut-off proves relevant to obtain near perfect fidelity for long simulations times in a single run. Overall our results exhibit a clear improvement based on a quantum model versus simulations based on a classical field approximation.

quant-ph↗

arXiv2021

Continuous multi-step pumping of the optical clock transition in alkaline-earth atoms with minimal perturbation

A suitable scheme to continuously create inversion on an optical clock transition with negligible perturbation is a key missing ingredient required to build an active optical atomic clock. Re- pumping of the atoms on the narrow transition typically needs several pump lasers in a multi step process involving several auxiliary levels. In general this creates large effective level shifts and a line broadening, strongly limiting clock accuracy. Here we present an extensive theoretical study for a realistic multi-level implementation in search of parameter regimes where a sufficient inversion can be achieved with minimal perturbations. Fortunately we are able to identify a useful operating regime, where the frequency shifts remain small and controllable, only weakly perturbing the clock transition for useful pumping rates. For practical estimates of the corresponding clock performance we introduce a straightforward mapping of the multilevel pump scheme to an effective energy shift and broadening parameters for the reduced two-level laser model system. This allows to evaluate the resulting laser power and spectrum using well-known methods.

quant-ph↗

arXiv2021

Nanoscale continuous quantum light sources based on driven dipole emitter arrays

Regular arrays of two-level emitters at distances smaller that the transition wavelength collectively scatter, absorb and emit photons. The strong inter-particle dipole coupling creates large energy shifts of the collective delocalized excitations, which generates a highly nonlinear response at the single and few photon level. This should allow to implement nanoscale non-classical light sources via weak coherent illumination. At the generic tailored examples of regular chains or polygons we show that the fields emitted perpendicular to the illumination direction exhibit a strong directional confinement with genuine quantum properties as antibunching. For short interparticle distances superradiant directional emission can enhance the radiated intensity by an order of magnitude compared to a single atom focused to a strongly confined solid angle but still keeping the anti-bunching parameter at the level of $g^{(2)}(0) \approx 10^{-2}$.

quant-ph↗

arXiv2021

A versatile quantum simulator for coupled oscillators using a 1D chain of atoms trapped near an optical nanofiber

The transversely confined propagating light modes of a nano-photonic optical waveguide or nanofiber can mediate effectively infinite-range forces. We show that for a linear chain of particles trapped within the waveguide's evanescent field, transverse illumination with a suitable set of laser frequencies should allow the implementation of a coupled-oscillator quantum simulator with time-dependent and widely controllable all-to-all interactions. At the example of the energy spectrum of oscillators with simulated Coulomb interactions we show that different effective coupling geometries can be emulated with high precision by proper choice of laser illumination conditions. Similarly, basic quantum gates can be selectively implemented between arbitrarily chosen pairs of oscillators in the energy basis as well as in a coherent-state basis. Key properties of the system dynamics and states can be monitored continuously by analysis of the out-coupled fiber fields.

quant-ph↗

arXiv2021

Continuous narrowband lasing with coherently driven V-level atoms

Simultaneous strong coherent pumping of the two transitions of a V-level atom with very differentdecay rates has been predicted to create almost perfect inversion on the narrower transition. Usingthe example of the blue and red transitions in Strontium we show that for suitable operatingconditions the corresponding resonant gain can be used to continuously operate a laser on thenarrow transition. In particular, for a strong detuning of the pump field with respect to the narrowtransition, coherent laser emission occurs close to the bare atomic transition frequency exhibitingonly a negligible contribution from coherent pump light scattered into the lasing mode.Calculations of the cavity output spectrum show that the resulting laser linewidth can get muchsmaller than the bandwidth of the pump light and even the natural linewidth of the narrow atomictransition. Its frequency is closely tied to the atomic transition frequency for properly chosen atomnumbers. Simulations including atomic motionshow Doppler cooling on the strong transitionwith minor motion heating on the lasing transition, so that continuous laser operation in thepresence of a magneto-optical trap should be possible with current experimental technology.

quant-ph↗

arXiv2020

Spin and density self-ordering in dynamic polarization gradients fields

We study the zero-temperature quantum phase diagram for a two-component Bose-Einstein condensate in an optical cavity. The two atomic spin states are Raman coupled by two transverse orthogonally-polarized, blue detuned plane-wave lasers inducing a repulsive cavity potential. For weak pump the lasers favor a state with homogeneous density and predefined uniform spin direction. When one pump laser is polarized parallel to the cavity mode polarization, the photons coherently scattered into the resonator induce a polarization gradient along the cavity axis, which mediates long-range density-density, spin-density, and spin-spin interactions. We show that the coupled atom-cavity system implements central aspects of the $t$-$J$-$V$-$W$ model with a rich phase diagram. At the mean-field limit we identify at least four qualitatively distinct density- and spin-ordered phases including ferro- and anti-ferromagnetic order along the cavity axis, which can be controlled via the pump strength and detuning. A real time observation of amplitude and phase of the emitted fields bears strong signatures of the realized phase and allows for real-time determination of phase transition lines. Together with measurements of the population imbalance most properties of the phase diagram can be reconstructed.

cond-mat.quant-gas↗

arXiv2020

Efficient frequency-selective single-photon antennas based on a bio-inspired nano-scale atomic ring design with 9-fold symmetry

Quantum emitters in confined arrays exhibit geometry dependent collective dynamics. In particular, nanoscopic regular polygon-shaped arrays can possess sub-radiant states with an exciton lifetime growing exponentially with emitter number. We show that by placing an extra resonant absorptive dipole at the ring center, such a structure becomes a highly efficient single-photon absorber with tailorable frequency. Interestingly, for exactly nine emitters in a nonagon, as it appears in a common biological light-harvesting complex (LHC2), we find a distinct minimum for its most dark state decay rate and a maximum of the effective absorption cross-section, surpassing that for a single absorptive emitter. The origin of this optimum for nine emitters can be geometrically traced to the fact that the sum of coupling strengths of a single ring emitter to all others including the center ring closely matches the coupling of the center to all ring emitters. The emerging dark collective eigenstate has dominant center occupation facilitating efficient energy absorption and fast transport. The resonance frequency can be tuned via ring size and dipole polarization. In analogy to parabolic antennas, the ring concentrates the incoming radiation at the center without being significantly excited, which minimizes transport loss and time.

quant-ph↗

arXiv2020

Many-Body Phases of a Planar Bose-Einstein Condensate with Cavity-Induced Spin-Orbit Coupling

We explore the many-body phases of a two-dimensional Bose-Einstein condensate with cavity-mediated dynamic spin-orbit coupling. By the help of two transverse non-interfering, counterpropagating pump lasers and a single standing-wave cavity mode, two degenerate Zeeman sub-levels of the quantum gas are Raman coupled in a double-$Λ$-configuration. Beyond a critical pump strength the cavity mode is populated via coherent superradiant Raman scattering from the two pump lasers, leading to the appearance of a dynamical spin-orbit coupling for the atoms. We identify three quantum phases with distinct atomic and photonic properties: the normal ``homogeneous'' phase, the superradiant ``spin-helix'' phase, and the superradiant ``supersolid spin-density-wave'' phase. The latter exhibits an emergent periodic atomic density distribution with an orthorhombic centered rectangular-lattice structure due to the interplay between the coherent photon scattering into the resonator and the collision-induced momentum coupling. The transverse lattice spacing of the emergent crystal is set by the dynamic spin-orbit coupling.

cond-mat.quant-gas↗

arXiv2020

Numerically exact treatment of many body self-organization in a cavity

We investigate the full quantum evolution of ultracold interacting bosonic atoms on a chain and coupled to an optical cavity. Extending the time-dependent matrix product state techniques and the many-body adiabatic elimination technique to capture the global coupling to the cavity mode and the open nature of the cavity, we examine the long time behavior of the system beyond the mean-field elimination of the cavity field. We investigate the many body steady states and the self-organization transition for a wide range of parameters. We show that in the self-organized phase the steady state consists in a mixture of the mean-field predicted density wave states and excited states with additional defects. In particular, for large dissipation strengths a steady state with a fully mixed atomic sector is obtained crucially different from the predicted mean-field state.

cond-mat.quant-gas↗

arXiv2020

Polarization Control of Radiation and Energy Flow in Dipole-Coupled Nanorings

Collective optical excitations in dipole-coupled nanorings of sub-wavelength spaced quantum emitters exhibit extreme sub-radiance and field confinement facilitating an efficient and low-loss ring-to-ring energy transfer. We show that energy shifts, radiative lifetimes, and emission patterns of excitons and biexcitons in such rings can be tailored via the orientation of the individual dipoles. Tilting the polarization from perpendicular to tangential to the ring dramatically changes the lifetime of the symmetric exciton state from superradiance to subradiance with the radiated field acquiring orbital angular momentum. At a magic tilt angle all excitons are degenerate and the transport fidelity between two rings exhibits a minimum. Further simulations suggest that, for certain parameters, the decay decreases double-exponentially with the emitter's density. Disorder in the rings' structure can even enhance radiative lifetimes. The transport efficiency strongly depends on polarization and size, which we demonstrate by simulating a bio-inspired example of two rings with 9 and 16 dipoles as found in biological light harvesting complexes (LHC). The field distribution in the most superradiant state in a full LHC multi-ring structure shows tight sub-wavelength field confinement in the central ring, while long-lived subradiant states store energy in the outer rings.

quant-ph↗

arXiv2020

A Nanoscale Coherent Light Source

Generically, a laser is composed of an optical resonator coupled to a gain medium. If the light amplification via stimulated emission dominates the mirror losses, the emitted light is coherent. Recent studies have shown that sub-wavelength sized rings of quantum emitters possess subradiant eigenmodes which mimic high-Q optical resonators. We add a continuously pumped atom as a gain medium in the ring's center creating a minimalistic coherent light source. The system behaves like a thresholdless laser, featuring a narrow linewidth well below the natural linewidth of the constituent atoms.

quant-ph↗

arXiv2020

The Hofstadter Butterfly in a Dynamic Cavity-Induced Synthetic Magnetic Field

Energy bands of electrons in a square lattice potential threaded by a uniform magnetic field exhibit a fractal structure known as the Hofstadter butterfly. Here we study a Fermi gas in a 2D optical lattice within a linear cavity with a tilt along the cavity axis. The hopping along the cavity axis is only induced by resonant Raman scattering of transverse pump light into a standing wave cavity mode. Choosing a suitable pump geometry allows to realize the Hofstadter-Harper model with a cavity-induced dynamical synthetic magnetic field, which appears at the onset of the superradiant phase transition. The dynamical nature of this cavity-induced synthetic magnetic field arises from the delicate interplay between collective superradiant scattering and the underlying fractal band structure. Using a sixth-order expansion of the free energy as function of the order parameter and by numerical simulations we show that at low magnetic fluxes the superradiant ordering phase transition is first order, while it becomes second order for higher flux. The dynamic nature of the magnetic field induces a non-trivial deformation of the Hofstadter butterfly in the superradiant phase. At strong pump far above the self-ordering threshold we recover the Hofstadter butterfly one would obtain in a static magnetic field.

cond-mat.quant-gas↗

arXiv2019

Self-ordering and cavity cooling using a train of ultrashort pulses

A thin atomic gas in an optical resonator exhibits a phase transition from a homogeneous density to crystalline order when laser illuminated orthogonal to the resonator axis. We study this well-known self-organization phenomenon for a generalized pumping scheme using a femtosecond pulse train with a frequency spectrum spanning a large bandwidth covering many cavity modes. We show that due to simultaneous scattering into adjacent longitudinal cavity modes the induced light forces and the atomic dynamics becomes nearly translation-invariant along the cavity axis. In addition the laser bandwidth introduces a new correlation length scale within which clustering of the atoms is energetically favorable. Numerical simulations allow us to determine the self-consistent ordering threshold power as function of bandwidth and atomic cloud size. We find strong evidence for a change from a second order to a first order self-ordering phase transition with growing laser bandwidth when the size of the atomic cloud gets bigger than the clustering length. An analysis of the cavity output reveals a corresponding transition from a single to a double pulse traveling within the cavity. This doubles the output pulse repetition rate and creates a new time crystal structure in the cavity output. Simulations also show that multi-mode operation significantly improves cavity cooling generating lower kinetic temperatures at a much faster cooling rate.

quant-ph↗

arXiv2019

Superradiant Cooling, Trapping, and Lasing of Dipole-Interacting Clock Atoms

A cold atomic gas with an inverted population on a transition coupled to a field mode of an optical resonator constitutes a generic model of a laser. For quasi-continuous operation, external pumping, trapping and cooling of the atoms is required to confine them in order to achieve enough gain inside the resonator. As inverted atoms are high-field seekers in blue detuned light fields, tuning the cavity mode to the blue side of the atomic gain transition allows for combining lasing with stimulated cavity cooling and dipole trapping of the atoms at the antinodes of the laser field. We study such a configuration using a semiclassical description of particle motion along the cavity axis. In extension of earlier work we include free space atomic and cavity decay as well as atomic dipole-dipole interactions and their corresponding forces. We show that for a proper choice of parameters even in the bad cavity limit the atoms can create a sufficiently strong field inside the resonator such that they are trapped and cooled via the superradiant lasing action with less than one photon on average inside the cavity.

quant-ph↗

arXiv2019

Emergent Quasicrystalline Symmetry in Light-Induced Quantum Phase Transitions

The discovery of quasicrystals with crystallographically forbidden rotational symmetries has changed the notion of the ordering in materials, yet little is known about the dynamical emergence of such exotic forms of order. Here we theoretically study a nonequilibrium cavity-QED setup realizing a zero-temperature quantum phase transition from a homogeneous Bose-Einstein condensate to a quasicrystalline phase via collective superradiant light scattering. Across the superradiant phase transition, collective light scattering creates a dynamical, quasicrystalline optical potential for the atoms. Remarkably, the quasicrystalline potential is "emergent" as its eight-fold rotational symmetry is not present in the Hamiltonian of the system, rather appears solely in the low-energy states. For sufficiently strong two-body contact interactions between atoms, a quasicrystalline order is stabilized in the system, while for weakly interacting atoms the condensate is localized in one or few of the deepest minima of the quasicrystalline potential.

cond-mat.quant-gas↗

arXiv2019

Unraveling the quantum nature of atomic self-ordering in a ring cavity

Atomic self-ordering to a crystalline phase in optical resonators is a consequence of the intriguing non-linear dynamics of strongly coupled atom motion and photons. Generally the resulting phase diagrams and atomic states can be largely understood on a mean-field level. However, close to the phase transition point, quantum fluctuations and atom-field entanglement play a key role and initiate the symmetry breaking. Here we propose a modified ring cavity geometry, in which the asymmetry imposed by a tilted pump beam reveals clear signatures of quantum dynamics even in a larger regime around the phase transition point. Quantum fluctuations become visible both in the dynamic and steady-state properties. Most strikingly we can identify a regime where a mean-field approximation predicts a runaway instability, while in the full quantum model the quantum fluctuations of the light field modes stabilize uniform atomic motion. The proposed geometry thus allows to unveil the "quantumness" of atomic self-ordering via experimentally directly accessible quantities.

quant-ph↗

arXiv2019

A Quantum N-Queens Solver

The N-queens problem is to find the position of N queens on an N by N chess board such that no queens attack each other. The excluded diagonals N-queens problem is a variation where queens cannot be placed on some predefined fields along diagonals. This variation is proven NP-complete and the parameter regime to generate hard instances that are intractable with current classical algorithms is known. We propose a special purpose quantum simulator that implements the excluded diagonals N-queens completion problem using atoms in an optical lattice and cavity-mediated long-range interactions. Our implementation has no overhead from the embedding allowing to directly probe for a possible quantum advantage in near term devices for optimization problems.

quant-ph↗