We study a bulk fermionic dipolar molecular gas in the quantum degenerate regime confined in a two-dimensional geometry. We consider two rotational states that encode a spin 1/2 degree of freedom. We derive a long-range interacting XXZ model describing the many-body spin dynamics of the molecules valid in the regime where motional degrees of freedom are frozen. Due to the spatially extended nature of the harmonic oscillator modes, the interactions in the spin model are very long-ranged and the system behaves close to the collective limit, resulting in robust dynamics and generation of entanglement in the form of spin squeezing even at finite temperature and in presence of dephasing and chemical reactions. We demonstrate how the internal state structure can be exploited to realise time-reversal and enhanced metrological sensing protocols.
We study the effect of dipolar interactions on the level of squeezing in spin-1 Bose-Einstein condensates by using the single mode approximation. We limit our consideration to the $\mathfrak{su}(2)$ Lie subalgebra spanned by spin operators. The biaxial nature of dipolar interactions allows for dynamical generation of spin-squeezed states in the system. We analyze the phase portraits in the reduced mean-filed space in order to determine positions of unstable fixed points. We calculate numerically spin squeezing parameter showing that it is possible to reach the strongest squeezing set by the tw…
We study the quantum critical effect enhanced spin-nematic squeezing and quantum Fisher information (QFI) in the spin-1 dipolar atomic Bose-Einstein condensate. We show that the quantum phase transitions can improve the squeezing and QFI in the nearby regime of critical point, and the Heisenberg-limited high-precision metrology can be obtained. The different properties of the ground squeezing and entanglement under even and odd number of atoms are further analyzed, by calculating the exact analytical expressions.We also demonstrate the squeezing and entanglement generated by the spin-mixing dy…
We investigate the process of spin squeezing in a ferromagnetic dipolar spin-1 Bose-Einstein condensate under the driven oneaxis twisting scheme, with emphasis on the detrimental effect of noisy environments (stray magnetic fields) which completely destroy the spin squeezing. By applying concatenated dynamical decoupling pulse sequences with a moderate bias magnetic field to suppress the effect of the noisy environments, we faithfully reconstruct the spin squeezing process under realistic experimental conditions. Our noise-resistant method is ready to be employed to generate the spin squeezed …
We investigate the coupling of a nanomechanical oscillator in the quantum regime with molecular (electric) dipoles. We find theoretically that the cantilever can produce single-mode squeezing of the center-of-mass motion of an isolated trapped molecule and two-mode squeezing of the phonons of an array of molecules. This work opens up the possibility of manipulating dipolar crystals, which have been recently proposed as quantum memory, and more generally, is indicative of the promise of nanoscale cantilevers for the quantum detection and control of atomic and molecular systems.
We develop finite temperature theory for a trapped dipolar Bose gas including thermal exchange interactions. Previous treatments neglected these, difficult to compute, terms. We present a methodology for numerically evaluating the thermal exchange contributions, making use of cylindrical symmetry. We then investigate properties of the dipolar gas, including calculating the excitation spectrum over the full range of trap anisotropy. We evaluate the contributions due to thermal exchange noting that, under some regimes, these effects can be at least as significant as the direct interaction. We th…
Cold atoms from a magneto-optic trap have been used as a nonlinear medium in a nearly resonant cavity. Squeezing in a probe beam passing through the cavity was demonstrated. The measured noise reduction is 40% for free atoms and 20% for weakly trapped atoms.
We study the interaction of a nearly resonant linearly polarized laser beam with a cloud of cold cesium atoms in a high finesse optical cavity. We show theoretically and experimentally that the cross-Kerr effect due to the saturation of the optical transition produces quadrature squeezing on both the mean field and the orthogonally polarized vacuum mode. An interpretation of this vacuum squeezing as polarization squeezing is given and a method for measuring quantum Stokes parameters for weak beams via a local oscillator is developed.
We consider a system of laser-cooled ions in a linear harmonic trap and study the phenomenon of squeezing exchange between their internal and motional degrees of freedom. An interesting relation between the quantum noise reduction (squeezing) and the dynamical evolution is found when the internal and motional subsystems are prepared in properly squeezed (intelligent) states. Specifically, the evolution of the system is fully governed by the relative strengths of spectroscopic and motional squeezing, including the phenomenon of total cancellation of the interaction when the initial squeezing pa…
Mach-Zehnder interferometer, a powerful tool for a wide variety of measurements, has been realized with Bose-Einstein condensates in recent experiments. In this report, we propose and analyze a realizable scheme for performing a Heisenberg-limited Mach-Zehnder interferometry with dipolar spin-1 condensate. Based upon adiabatic processes of sweeping the transverse magnetic field, we demonstrate a perfect phase transition, which accomplishes the beam splitter, phase shifter and recombiner as for a Mach-Zehnder interferometer. The attractive dipolar interaction ensures the existence of a path-ent…
We propose a scheme to obtain the Heisenberg-limited parameter estimation precision by immersing atoms in a thermally equilibrated quasi-one-dimensional dipolar Bose-Einstein condensate reservoir. We show that the collisions between the dipolar atoms and the immersed atoms can result in a controllable nonlinear interaction through tuning the relative strength and the sign of the dipolar and contact interaction. We find that the repulsive dipolar interaction reservoir is preferential for the spin squeezing and the appearance of an entangled non-Gaussian state. As a useful resource for quantum m…
We propose an efficient method for controlled generation of field squeezing with cold atomic clouds trapped close to a superconducting transmission line resonator. It is shown that, based on the coherent strong magnetic coupling between the collective atomic spins and microwave fields in the transmission line resonator, two-mode or single mode field squeezed states can be generated through coherent control on the dynamics of the system. The degree of squeezing and preparing time can be directly controlled through tuning the external classical fields. This protocol may offer a promising platfor…
To establish an applicable system for advanced quantum information processing between light and atoms, we have demonstrated the quantum non-demolition (QND) measurement with a collective spin of cold ytterbium atoms (171Yb), and observed 1.8 (-1.5, +2.4) dB spin squeezing. Since a 171Yb atom has only a nuclear spin of 1/2 in the ground state, the system is the simplest spin ensemble and robust against decoherence. We used very short pulses with the width of 100 ns, so the interaction time became much shorter than the decoherence time, which is important for multi-step quantum information proce…
We study the conditions for generating spin squeezing via a quantum non-demolition measurement in an ensemble of cold 87Rb atoms. By considering the interaction of atoms in the 5S_{1/2}(F=1) ground state with probe light tuned near the D2 transition, we show that, for large detunings, this system is equivalent to a spin-1/2 system when suitable Zeeman substates and quantum operators are used to define a pseudo-spin. The degree of squeezing is derived for the rubidium system in the presence of scattering causing decoherence and loss. We describe how the system can decohere and lose atoms, and p…
We have investigated both theoretically and experimentally dipolar relaxation in a gas of magnetically trapped chromium atoms. We have found that the large magnetic moment of 6 $μ_B$ results in an event rate coefficient for dipolar relaxation processes of up to $3.2\cdot10^{-11}$ cm$^{3}$s$^{-1}$ at a magnetic field of 44 G. We present a theoretical model based on pure dipolar coupling, which predicts dipolar relaxation rates in agreement with our experimental observations. This very general approach can be applied to a large variety of dipolar gases.
We report the generation of a macroscopic singlet state in a cold atomic sample via quantum non-demolition (QND) measurement induced spin squeezing. We observe 3 dB of spin squeezing and detect entanglement of up to $5.5\times10^5 $ atoms with $5σ$ statistical significance using a generalized spin squeezing inequality. The degree of squeezing implies at least 50% of the atoms have formed singlets, while the response to a magnetic field gradient indicates entanglement bonds at all length scales, a characteristic of quantum spin liquids.
Planar squeezed states, i.e. quantum states which are squeezed in two orthogonal spin components, have recently attracted attention due to their applications in atomic interferometry and quantum information [Q. Y. He et al, New J. Phys. 14, 093012 (2012)]. While canonical variables such as quadratures of the radiation field can be squeezed in at most one component, simultaneous squeezing in two orthogonal spin components can be achieved due to the angular momentum commutation relations. We present a novel scheme for planar squeezing via quantum non-demolition (QND) measurements in spin-1 syste…
We investigate how entangled coherent states and superpositions of low intensity coherent states of non-Gaussian nature can be generated via non-resonant interaction between either two linearly or circularly polarized field modes and an ensemble of X-like four-level atoms placed in an optical cavity. We compare our results to recent experimental observations and argue that the non-Gaussian structure of the field states may be present in those systems.
We present a method for phase and number squeezing in two-mode Bose systems using dissipation. The effectiveness of this method is demonstrated by considering cold Bose gases trapped in a double-well potential. The extension of our formalism to an optical lattice gives control of the phase boundaries of the steady-state phase diagram, and we discover a new phase characterized by a non-zero condensate fraction and thermal-like particle-number statistics. We also show how to perform amplitude squeezing in a single-mode system using dissipation.
We extend the criteria for $k$-particle entanglement from the spin squeezing parameter presented in [A.S. Sørensen and K. Mølmer, Phys. Rev. Lett. {\bf 86}, 4431 (2001)] to systems with a fluctating number of particles. We also discuss how other spin squeezing inequalities can be generalized to this situation. Further, we give an operational meaning to the bounds for cases where the individual particles cannot be addressed. As a by-product, this allows us to show that in spin squeezing experiments with cold gases the particles are typically distinguishable in practise. Our results justify the …
We demonstrate a cooperative optical non-linearity caused by dipolar interactions between Rydberg atoms in an ultra-cold atomic ensemble. By coupling a probe transition to the Rydberg state we map the strong dipole-dipole interactions between Rydberg pairs onto the optical field. We characterize the non-linearity as a function of electric field and density, and demonstrate the enhancement of the optical non-linearity due to cooperativity.
We investigate many-body spin squeezing dynamics in an XXZ model with interactions that fall off with distance $r$ as $1/r^α$ in $D=2$ and $3$ spatial dimensions. In stark contrast to the Ising model, we find a broad parameter regime where spin squeezing comparable to the infinite-range $α=0$ limit is achievable even when interactions are short-ranged, $α>D$. A region of "collective" behavior in which optimal squeezing grows with system size extends all the way to the $α\to\infty$ limit of nearest-neighbor interactions. Our predictions, made using the discrete truncated Wigner approximation (D…
We calculate the energy and wave functions of two particles confined to two spatial dimensions interacting via arbitrary anisotropic potentials with negative or zero net volume. The general rigorous analytic expressions are given in the weak coupling limit where universality or model independence are approached. The monopole part of anisotropic potentials is crucial in the universal limit. We illustrate the universality with a system of two arbitrarily polarized cold dipolar molecules in a bilayer. We discuss the transition to universality as function of polarization and binding energy, and co…
We consider the N-body problem in a layered geometry containing cold polar molecules with dipole moments that are polarized perpendicular to the layers. A harmonic approximation is used to simplify the hamiltonian and bound state properties of the two-body inter-layer dipolar potential are used to adjust this effective interaction. To model the intra-layer repulsion of the polar molecules, we introduce a repulsive inter-molecule potential that can be parametrically varied. Single chains containing one molecule in each layer, as well as multi-chain structures in many layers are discussed and th…
Reaching high densities is a key step towards cold-collision experiments with polyatomic molecules. We use a cryofuge to load up to 2$\times10^7$ CH$_3$F molecules into a box-like electric trap, achieving densities up to 10$^7$/cm$^3$ at temperatures around 350 mK where the elastic dipolar cross-section exceeds 7$\times$10$^{-12}$cm$^2$. We measure inelastic rate constants below 4$\times$10$^{-8}$cm$^3$/s and control these by tuning a homogeneous electric field that covers a large fraction of the trap volume. Comparison to ab-initio calculations gives excellent agreement with dipolar relaxatio…
We study the process of squeezing of an ensemble of cold atoms in a pulsed optical lattice. The problem is treated both classically and quantum-mechanically under various thermal conditions. We show that a dramatic compression of the atomic density near the minima of the optical potential can be achieved with a proper pulsing of the lattice. Several strategies leading to the enhanced atomic squeezing are suggested, compared and optimized.
We investigate theoretically and experimentally a nondestructive interferometric measurement of the state population of an ensemble of laser cooled and trapped atoms. This study is a step towards generation of (pseudo-) spin squeezing of cold atoms targeted at the improvement of the Caesium clock performance beyond the limit set by the quantum projection noise of atoms. We calculate the phase shift and the quantum noise of a near resonant optical probe pulse propagating through a cloud of cold 133Cs atoms. We analyze the figure of merit for a quantum non-demolition (QND) measurement of the col…
We study a production of spin-squeezed states with ultra-cold atomic fermions described by the Fermi-Hubbard model in the Mott insulating phase. We show activation of two twisting mechanisms by a position-dependent laser coupling between internal degrees of freedom of atoms. A single laser coupling simulates the one-axis twisting model with the orientation of the twisting axis determined by the coupling phase. Adding a second laser beam with a properly chosen phase paves the way to simulate the two-axis counter-twisting model, enabling to approach the Heisenberg-limited level of squeezing.
Finite fermion systems are known to exhibit shell structure in the weakly-interacting regime, as well known from atoms, nuclei, metallic clusters or even quantum dots in two dimensions. All these systems have in common that the particle interactions between electrons or nucleons are spatially isotropic. Dipolar quantum systems as they have been realized with ultra-cold gases, however, are governed by an intrinsic anisotropy of the two-body interaction that depends on the orientation of the dipoles relative to each other. Here we investigate how this interaction anisotropy modifies the shell st…
We present a method to design a finite decay rate for excited rotational states in polar molecules. The setup is based on a hybrid system of polar molecules with atoms driven into a Rydberg state. The atoms and molecules are coupled via the strong dipolar exchange interaction between two rotation levels of the polar molecule and two Rydberg states. Such a controllable decay rate opens the way to optically pump the hyperfine levels of polar molecules and it enables the application of conventional laser cooling techniques for cooling polar molecules into quantum degeneracy.
The scalable production of multipartite entangled states in ensembles of qubits is a fundamental function of quantum devices, as such states are an essential resource both for fundamental studies on entanglement, as well as for applied tasks. Here we focus on the $U(1)$ symmetric Hamiltonians for qubits with dipolar interactions -- a model realized in several state-of-the-art quantum simulation platforms for lattice spin models, including Rydberg-atom arrays with resonant interactions. Making use of exact and variational simulations, we theoretically show that the non-equilibrium dynamics gene…
We report on the generation of non separable beams produced via the interaction of a linearly polarized beam with a cloud of cold cesium atoms placed in an optical cavity. We convert the squeezing of the two linear polarization modes into quadrature entanglement and show how to find out the best entanglement generated in a two-mode system using the inseparability criterion for continuous variable [Duan et al., Phys. Rev. Lett. 84, 2722 (2000)]. We verify this method experimentally with a direct measurement of the inseparability using two homodyne detections. We then map this entanglement into …
Strongly correlated quantum systems can exhibit exotic behavior controlled by topology. We predict that the ν=1/2 fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins. As a specific implementation, we analyze how to prepare and detect synthetic gauge potentials for the rotational excitations of ultra-cold polar molecules trapped in a deep optical lattice. While the orbital motion of the molecules is pinned, at finite densities, the rotational excitations form a fractional Chern insulator. We present a detailed experimental blueprint for KR…
We consider a quantum Otto cycle operating between two squeezed thermal reservoirs. The influences of the squeezing degree on the optimization performance of quantum Otto heat engines and refrigerators are investigated. We demonstrate that under symmetric condition, the efficiency at maximum power (EMP) of heat engines and the coefficient of performance (COP) at maximum \c{hi} criterion of refrigerators are equal to Curzon-Ahlborn (CA) efficiency and CA COP, respectively. We also found that under asymmetric condition, the EMP of heat engines can be improved when the squeezing degree of hot the…
This dissertation studies spin squeezing, entanglement and decoherence in large ensembles of cold, trapped alkali atoms with hyperfine spin f interacting with optical fields. Restricting the state of each atom to a qutrit embedded in the 2f+1 dimensional hyperfine spin enables us to efficiently model the coherent and dissipative dynamics of the ensemble. This formalism also allows us to explore the effects of local control on the internal hyperfine spins of the atoms. State preparation using such control increases the entangling power of the atom-light interface for f>1/2. Subsequent control o…
We propose and analyze a physical system that naturally admits two-dimensional topological nearly flat bands. Our approach utilizes an array of three-level dipoles (effective S = 1 spins) driven by inhomogeneous electromagnetic fields. The dipolar interactions produce arbitrary uniform background gauge fields for an effective collection of conserved hardcore bosons, namely, the dressed spin-flips. These gauge fields result in topological band structures, whose bandgap can be larger than the corresponding bandwidth. Exact diagonalization of the full interacting Hamiltonian at half-filling revea…
We analyze theoretically polar molecules confined in planar arrays of one dimensional tubes. In the classical limit, if the number of tubes is finite, new types of "clustered Wigner crystals" with increasingly many molecules per unit cell can be stabilized by tuning the in-plane angle between the dipolar moments and the tube direction. Quantum mechanically, these phases melt into distinct "clustered Luttinger liquids." We calculate the phase diagram of the system and study the quantum melting of the clustered phases. We find that the requirements for exploring these phases are reachable in cur…
We show that ultracold two-component fermionic dipolar gases in an optical lattice with strong two-body on-site loss can be used to realize a tunable effective spin-one model. Fermion number conservation provides an unusual constraint that $\sum_i (S^z_i)^2$ is conserved, leading to a novel topological liquid phase in one dimension which can be thought of as the gapless analog of the Haldane gapped phase of a spin-one Heisenberg chain. The properties of this phase are calculated numerically via the infinite time-evolving block decimation method and analytically via a mapping to a one-mode Lutt…
Many-body entangled states are key elements in quantum information science and quantum metrology. One important problem in establishing a high degree of many-body entanglement using optical techniques is the leakage of the system information via the light that creates such entanglement. We propose an all-optical interference-based approach to erase this information. Unwanted atom-light entanglement can be removed by destructive interference of three or more successive atom-light interactions, with only the desired effective atom-atom interaction left. This quantum erasure protocol allows imple…
The Stokes and anti-Stokes components of the spectrum of resonance fluorescence of a single trapped atom, which originate from the mechanical coupling between the scattered photons and the quantized motion of the atomic center of mass, exhibit quantum correlations which are of two-mode-squeezing type. We study and demonstrate the build-up of such correlations in a specific setup, which is experimentally accessible, and where the atom acts as efficient and continuous source of EPR-entangled, two-mode squeezed light.
We consider a finite-time quantum Otto heat engine that consists of two isochoric (thermal-contact) process, where the system is alternatively coupled to a hot squeezed and a cold thermal reservoir, and two unitary driven strokes, where the system is isolated from these two baths and its von Neumann entropy keeps constant. Both quantum inner friction and coherence are generated along the driven stroke and coherence cannot be fully erased after the finite-time hot isochore. Using full counting statistics, we present the probability distribution functions of heat injection and total work per cyc…
