The equations of motion for the molecular rotation are derived for vibrationally cold dimers that are polarized by off-resonant laser light. It is shown that, by eliminating electronic and vibrational degrees of freedom, a quantum master equation for the reduced rotational density operator can be obtained. The coherent rotational dynamics is caused by stimulated Raman transitions, whereas spontaneous Raman transitions lead to decoherence in the motion of the quantized angular momentum. As an example the molecular dynamics for the optical Kerr effect is chosen, revealing decoherence and heating of the molecular rotation.
We present the quantum master equation describing the coherent and incoherent dynamics of a rapidly rotating molecule in presence of a thermal background gas. The master equation relates the rate of rotational alignment decay and decoherence to the microscopic scattering amplitudes, which we calculate for anisotropic van der Waals scattering. For large rotational energies, we find excellent agreement of the resulting alignment decay rate with recent superrotor experiments.
A Ramsey-type interferometer is suggested, employing a cold trapped ion and two time-delayed off-resonant femtosecond laser pulses. The laser light couples to the molecular polarization anisotropy, inducing rotational wavepacket dynamics. An interferogram is obtained from the delay dependent populations of the final field-free rotational states. Current experimental capabilities for cooling and preparation of the initial state are found to yield an interferogram visibility of more than 80\%. The interferograms can be used to determine the polarizability anisotropy with an accuracy of about $\p…
We present the Markovian quantum master equation describing rotational decoherence, friction, diffusion, and thermalization of planar, linear, and asymmetric rotors in contact with a thermal environment. It describes how an arbitrary initial rotation state decoheres and evolves toward a Gibbs-like thermal ensemble, as we illustrate numerically for the linear and the planar top, and it yields the expected rotational Fokker-Planck equation of Brownian motion in the semiclassical limit.
We deduce the coherent backscattering signal from two distant laser-driven atoms using single-atom equations. In contrast to the standard master equation treatment, this new approach is suitable for the generalization to a large number of atomic scatterers.
Sympathetic cooling of trapped ions has been established as a powerful technique for manipulation of non-laser-coolable ions (Raizen1992,Waki1992,Bowe1999,Barrett2003). For molecular ions, it promises vastly enhanced spectroscopic resolution and accuracy. However, this potential remains untapped so far, with the best resolution achieved being not better than $5\times10^{-8}$ fractionally, due to residual Doppler broadening being present in ion clusters even at the lowest achievable translational temperatures (Bressel2012). Here we introduce a general and accessible approach that enables Dopple…
Cold collisions of light molecules are often dominated by a single partial wave resonance. For the rotational quenching of HD(v=1,j=2) by collisions with ground state para-H2, the process is dominated by a single L=2 partial wave resonance centered around 0.1 K. Here, we show that this resonance can be switched on or off simply by appropriate alignment of the HD rotational angular momentum relative to the initial velocity vector, thereby enabling complete control of the collision outcome.
We have obtained general expressions for the intensity of radiation and tangential force of a small polarizable particle in the process of translational-rotational motion in equilibrium radiation background (thermalized photon gas) of certain temperature at an arbitrary relative orientation of the linear and angular velocity vectors. It is shown that in cold vacuum background the translational velocity of particle is independent of time and the intensity of its spontaneous emission is determined by the angular velocity and imaginary part of the polarizability.
Controlling the internal degrees of freedom is a key challenge for applications of cold and ultracold molecules. Here, we demonstrate rotational-state cooling of trapped methyl fluoride molecules (CH3F) by optically pumping the population of 16 M-sublevels in the rotational states J=3,4,5, and 6 into a single level. By combining rotational-state cooling with motional cooling, we increase the relative number of molecules in the state J=4, K=3, M=4 from a few percent to over 70%, thereby generating a translationally cold (~30mK) and nearly pure state ensemble of about 10^6 molecules. Our scheme …
We consider a measurement of the position of a spot painted on the surface of a trapped nano-optomechanical sphere. The measurement extracts information about the position of the spot and in doing so measures a combination of the orientation and position of the sphere. The quantum back-action of the measurement entangles and correlates these two degrees of freedom. Such a measurement is not available for atoms or ions, and provides a mechanism to probe the quantum mechanical properties of trapped optomechanical spheres. In performing simulations of this measurement process we also test a numer…
Resonances are associated with the trapping of an intermolecular complex, and are characterized by a series of quantum numbers such as the total angular momentum and the parity, representative of a specific partial wave. Here we show how at cold temperatures the rotational quenching of HF(j=1,2) with H is strongly influenced by the presence of manifolds of resonances arising from the combination of a single value of the orbital angular momentum with different total angular momentum values. These resonances give rise up to a two-fold increase in the thermal rate coefficient at the low temperatu…
The electrostatic interaction between an excited atom and a diatomic ground state molecule in an arbitrary rovibrational level at large mutual separations is investigated with a general second-order perturbation theory, in the perspective of modeling the photoassociation between cold atoms and molecules. We find that the combination of quadrupole-quadrupole and van der Waals interactions compete with the rotational energy of the dimer, limiting the range of validity of the perturbative approach to distances larger than 100 a.u.. Numerical results are given for the long-range interaction betwee…
A cloud of cold N two-level atoms driven by a resonant laser beam shows cooperative effects both in the scattered radiation field and in the radiation pressure force acting on the cloud center-of-mass. The induced dipoles synchronize and the scattered light presents superradiant and/or subradiant features. We present a quantum description of the process in terms of a master equation for the atomic density matrix in the scalar, Born-Markov approximations, reduced to the single-excitation limit. From a perturbative approach for weak incident field, we derive from the master equation the effectiv…
We describe a simple scheme for the implementation and control of effective spin-spin interactions in self-assembled crystals of cold polar molecules. In our scheme spin states are encoded in two long-lived rotational states of the molecules and coupled via state dependent dipole-dipole forces to the lattice vibrations. We show that by choosing an appropriate time dependent modulation of the induced dipole moments the resulting phonon-mediated interactions compete with the direct dipole-dipole coupling and lead to long-range and tunable spin-spin interaction patterns. We illustrate how this te…
A Bose-Hubbard Hamiltonian, modeling cold bosons in an optical lattice, is used to simulate the dynamics of interacting open quantum systems as subsystems a larger closed system, avoiding complications like the introduction of baths, complex absorbing potentials or absorbing boundaries. The numerically exact unitary dynamics is compared with effective descriptions of the subsystems based on non-Hermitian Hamiltonians or Lindblad master equations. The validity of popular models with constant decay rates is explicitly analyzed for decaying single and double wells. In addition we present a discre…
We study the rotational and vibrational heating of diatomic molecules placed near a surface at finite temperature on the basis of macroscopic quantum electrodynamics. The internal molecular evolution is governed by transition rates that depend on both temperature and position. Analytical and numerical methods are used to investigate the heating of several relevant molecules near various surfaces. We determine the critical distances at which the surface itself becomes the dominant source of heating and we investigate the transition between the long-range and short-range behaviour of the heating…
We outline the non-perturbative theory of multiple scattering of resonant, intense laser light off a dilute cloud of cold atoms. A combination of master equation and diagrammatic techniques allows, for the first time, a quantitative description of nonlinear diffusive transport as well as of coherent backscattering of the injected electromagnetic field, notwithstanding the exponential growth of Hilbert space with the number of atomic scatterers. As an exemplary application, we monitor the laser light's intensity profile within the medium, the spectrum of the backscattered light and the coherent…
We investigate the problem of a single ion in a radio-frequency trap and immersed in an ultracold Bose gas either in a condensed or a non-condensed phase. We develop master equation formalism describing the sympathetic cooling and we determine the cooling rates of ions. We show that cold atomic reservoir modifies the stability diagram of the ion in the Paul trap creating the regions where the ion is either cooled or heated due to the energy quanta exchanged with the time-dependent potential.
We analyze the continuous monitoring of a qudit coupled to a cavity using both phase-preserving and phase-sensitive amplification. The quantum trajectories of the system are described by a stochastic master equation, for which we derive the appropriate Lindblad operators. The measurement back-action causes spiraling in the state coordinates during collapse, which increases as the system levels become less distinguishable. We discuss two examples: a two-level system and an $N$-dimensional system and meter with rotational symmetry in the quadrature space. We also provide a comparison of the effe…
Quantum calculations are reported for the stereodynamic control of the H + D$_{2}\longleftrightarrow$ D + HD chemical reaction in the energy range of 1-50 K. Stereodynamic control is achieved by a formalism similar to that reported by Perreault et al. [Nature Chem. 10, 561 (2018)] in recent experimental works in which the alignment of the molecular bond axis relative to the incident relative velocity is controlled by selective preparations of the molecule in a specific or superposition of magnetic projection quantum numbers of the initial molecular rotational level. The approach presented here…
We consider a rotationally invariant system-bath (RISB) model in three-dimensional space that is described by a linear-rigid rotor independently coupled to three sets of harmonic-oscillator baths as functions of the Euler angle. While this model has been developed to study a dielectric relaxation of a dipolar molecule in solvation as a problem of classical Debye relaxation, here we investigate it as a problem of open quantum dynamics as an extension of our previous work [J. Chem. Phys, 149, 084110 (2018)], in which we studied a two-dimensional (2D) RISB model, to a three-dimensional (3D) RISB …
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.
We present the Born-Markov approximated Redfield quantum master equation (RQME) description for an open system of non-interacting particles (bosons or fermions) on an arbitrary lattice of $N$ sites in any dimension and weakly connected to multiple reservoirs at different temperatures and chemical potentials. The RQME can be reduced to the Lindblad equation, of various forms, by making further approximations. By studying the $N=2$ case, we show that RQME gives results which agree with exact analytical results for steady state properties and with exact numerics for time-dependent properties, ove…
We discuss the rotational cooling of diatomic molecules in a Bose-Einstein condensate (BEC) of ultra-cold atoms by emission of phonons with orbital angular momentum. Despite the superfluidity of the BEC there is no frictionless rotation for typical molecules since the dominant cooling occurs via emission of particle-like phonons. Only for macro-dimers, whose size becomes comparable or larger than the condensate healing length, a Landau-like, critical angular momentum exists below which phonon emission is suppressed. We find that the rotational relaxation of typical molecules is in general fast…
Anisotropy is a fundamental property of particle interactions. It occupies a central role in cold and ultra-cold molecular processes, where long range forces have been found to significantly depend on orientation in ultra-cold polar molecule collisions. Recent experiments have demonstrated the emergence of quantum phenomena such as scattering resonances in the cold collisions regime due to quantization of the intermolecular degrees of freedom. Although these states have been shown to be sensitive to interaction details, the effect of anisotropy on quantum resonances has eluded experimental obs…
Erik Verlinde's theory of entropic gravity [arXiv:1001.0785], postulating that gravity is not a fundamental force but rather emerges thermodynamically, has garnered much attention as a possible resolution to the quantum gravity problem. Some have ruled this theory out on grounds that entropic forces are by nature noisy and entropic gravity would therefore display far more decoherence than is observed in ultra-cold neutron experiments. We address this criticism by modeling linear gravity acting on small objects as an open quantum system. In the strong coupling limit, when the model's unitless f…
We show that an ensemble of polar molecules trapped in an optical lattice can be considered as a controllable open quantum system. The coupling between collective rotational excitations and the motion of the molecules in the lattice potential can be controlled by varying the strength and orientation of an external DC electric field as well as the intensity of the trapping laser. The system can be described by a generalized Holstein Hamiltonian with tunable parameters and can be used as a quantum simulator of excitation energy transfer and polaron phenomena. We show that the character of excita…
We present precision spectroscopy on electrically trapped formaldehyde (H$_2$CO), demonstrating key attributes which will enable molecular spectroscopy with unprecedented precision. Our method makes use of a microstructured electric trap with homogeneous fields in the trap center and rotational transitions with minimal Stark broadening at a 'magic' offset electric field. Using molecules cooled to the low millikelvin temperature regime via optoelectrical Sisyphus cooling, we reduce Stark broadening on the $J=5\leftarrow4$ ($K=3$) transition at 364 GHz to well below 1 kHz, observe Doppler-limite…
Energy transfer through quantum coherences plays an essential role in diverse natural phenomena and technological applications, such as human vision, light-harvesting complexes, quantum heat engines, and quantum information and computing. The understanding of the long-lived coherence involved in these phenomena requires a detailed modeling of the system-bath interactions beyond the so-called secular and/or Markovian approximations. Despite continuous theoretical progress on understanding nonsecular dynamics in the last decades, convincing experimental observations are still lacking. By using t…
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 entangle…
One of the main goals of chemical dynamics is the creation of molecular beams composed of a single (vibrational, rotational, and magnetic) quantum state of choice. In this paper we show that it is possible to achieve {\it complete} quantum state selectivity by producing resistance to electromagnetically induced deflection (EID) and that the state to be selected can be "dialed in" at will. We illustrate the method by showing in detail how to purify thermal beams of the LiRb and IF molecules to yield molecular beams composed of a variety of pre-chosen single internal quantum states and/or superp…
Master Equation for a Quantum Gas of Polarizable Particles in Cavities
Universität des Saarlandes（萨尔兰大学）；University of Geneva（日内瓦大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Eidgenössische Technische Hochschule Zürich（苏黎世联邦理工学院）；University of Bonn（波恩大学）
The recent experimental realization of cold polar molecules in the rotational and vibrational ground state opens the door to the study of a wealth of phenomena involving long-range interactions. By applying an optical lattice to a gas of cold polar molecules one can create a layered system of planar traps. Due to the long-range dipole-dipole interaction one expects a rich structure of bound complexes in this geometry. We study the bilayer case and determine the two-body bound state properties as a function of the interaction strength. The results clearly show that a least one bound state will …
We study the non-equilibrium dynamics of Axion-like particles (ALP) coupled to Standard Model degrees of freedom in thermal equilibrium. The Quantum Master Equation (QME) for the (ALP) reduced density matrix is derived to leading order in the coupling of the (ALP) to the thermal bath, but to \emph{all} orders of the bath couplings to degrees of freedom within or beyond the Standard Model other than the (ALP). The (QME) describes the damped oscillation dynamics of an initial misaligned (ALP) condensate, thermalization with the bath, decoherence and entropy production within a unifying framework…
We calculate properties of dipolar interacting ultracold molecules or Rydberg atoms in a semi-synthetic three-dimensional configuration -- one synthetic dimension plus a two-dimensional real space optical lattice or periodic microtrap array -- using the stochastic Green function Quantum Monte Carlo method. Through a calculation of thermodynamic quantities and appropriate correlation functions, along with their finite size scalings, we show that there is a second order transition to a low temperature phase in which two-dimensional `sheets' form in the synthetic dimension of internal rotational …
Evaluating the time-dependent dynamics of driven open quantum systems is relevant for a theoretical description of many systems, including molecular junctions, quantum dots, cavity-QED experiments, cold atoms experiments and more. Here, we formulate a rigorous microscopic theory of an out-of-equilibrium open quantum system of non-interacting particles on a lattice weakly coupled to multiple baths and driven by periodically varying thermodynamic parameters like temperature and chemical potential of the bath. The particles can be either bosonic or fermionic and the lattice can be of any dimensio…
The periodically kicked quantum rotor is known for non-classical effects such as quantum localisation in angular momentum space or quantum resonances in rotational excitation. These phenomena have been studied in diverse systems mimicking the kicked rotor, such as cold atoms in optical lattices, or coupled photonic structures. Recently, it was predicted that several solid state quantum localisation phenomena - Anderson localisation, Bloch oscillations, and Tamm-Shockley surface states - may manifest themselves in the rotational dynamics of laser-kicked molecules. Here, we report the first obse…
