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arXiv:1512.08430 · Physical Review A

Collisional decoherence of polar molecules

Kai Walter, Benjamin A. Stickler, Klaus Hornberger

Published Jun 10, 2016• 14 citations
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Abstract

The quantum state of motion of a large and rotating polar molecule can lose coherence through the collisions with gas atoms. We show how the associated quantum master equation for the center of mass can be expressed in terms of the orientationally averaged differential and total scattering cross sections, for which we provide approximate analytic expressions. The master equation is then utilized to quantify collisional decoherence in a interference experiment with polar molecules.

DOI
10.1103/physreva.93.063612

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The quantum state of motion of a large and rotating polar molecule can lose coherence through the collisions with gas atoms. We show how the associated quantum master equation for the center of mass can be expressed in terms of the orientationally averaged differential and total scattering cross sections, for which we provide approximate analytic expressions. The master equation is then utilized to quantify collisional decoherence in a interference experiment with polar molecules.
The present thesis deals with two main topics. First, I study in detail the interaction of a delocalized molecular matter-wave with a standing-wave laser grating. Due to absorption of photons in an optical grating, molecules can get excited and numerous internal photophysical processes are induced. For the theoretical description of the molecule-light interaction I take three relevant internal molecular processes into account: intersystem crossing, fluorescence and internal conversion. Furthermore, the fact that molecules can change their optical properties because of the photoexcitation is shown to have a measurable effect on matter-wave interferometry. The second topic of this thesis is about collisions between a polar molecule and non-polar environmental gas atoms, and their effects on the coherence of the center-of-mass state. Because the scattering potential depends on the molecular orientation the molecular rotational state must also be considered. Assuming a slow rotation of the molecule compared to the scattering time and that the molecular mass fairly exceeds the mass of a gas atom, I present a master equation of collisional decoherence, which depends on the molecular orientation. Its predictions for matter-wave interferometry are discussed both in the near and far field.
We study the fully itinerant dynamics of ultracold but nondegenerate polar molecules with a spin-1/21/21/2 degree of freedom encoded into two of their electric field dressed rotational states. Center-of-mass molecular motion is constrained to two dimensions via tight confinement with a one-dimensional optical lattice, but remains mostly unconstrained within the plane. The pseudospins can become entangled through ultracold dipolar collisions, for which the locality of interactions is greatly relaxed by free molecular motion. At the level of single-molecule observables, collision-induced entanglement manifests as spin decoherence, for which our theoretical calculations serve well to describe recent Ramsey contrast measurements of quasi-two-dimensional confined KRb molecules at JILA [A. Carroll et al., Science 388, 6745 (2025)]. In presenting a more detailed theoretical analysis of the KRb experiment, we highlight a key finding that molecular loss enhanced by particle exchange symmetry can lead to a suppression of collective spin decoherence, a mechanism we refer to as ``loss-induced quantum autoselection.'' We then show that, by utilizing bialkali species with sufficiently large dipole moments, loss can be near completely suppressed in all collision channels via electric field tunable confinement-induced collisional shielding. The afforded collisional stability permits fully coherent spin mixing dynamics, natively realizing unitary circuit dynamics with random all-to-all connectivity and U(1) charge conservation. This work establishes a bridge between the domains of ultracold molecular collisions and many-body spin physics, ultimately proposing the use of nondegenerate bulk molecular gases as a controllable platform for nonequilibrium explorations of itinerant quantum matter.
We explore the total collisional cross section of ground-state polar molecules in an electric field at various energies, focusing on RbCs\mathrm{RbCs}RbCs and RbK\mathrm{RbK}RbK. An external electric field polarizes the molecules and induces strong dipolar interactions, leading to nonzero partial waves contributing to the scattering even as the collision energy goes to zero. This results in the need to compute scattering problems with many different values of total MMM to converge the total cross section. An accurate and efficient approximate total cross section is introduced and used to study the low-field temperature dependence. To understand the scattering of the polar molecules we compare a semiclassical cross section with the quantum unitarity limit. This comparison leads to the ability to characterize the scattering based on the value of the electric field and the collision energy. General and simple forms of the characteristic electric field and energy are given, enabling characterization of the scattering.
The response of a collision-broadened gas sample to driving coherent radiation is studied theoretically, taking into account effects of coherent excitations of two or more atoms (or molecules). In analogy to the Bloch-type master equation for one-atom coherences, describing the motion of a single atom "dressed" by the relevant (incident and detected) field modes, a master equation is derived for two-atom coherences, including an effective interaction of the Bethe-Salpeter---type, accounting for the mutual interaction of the coherently driven pair. The master equation includes also all symmetrization effects owing to resonance exchange between identical atoms, and is limited to nonreactive gas atoms (or molecules) undergoing binary collisions, including otherwise all (internal and translational) relaxation effects. The self-energy kernels are expressed in a nonperturbative fashion, in terms of binary-collision scattering amplitudes, and include renormalization effects due to coincidence of radiative couplings with the collisions (optical and radiative collisions). The concept of two-atom coherences is generalized to higher coherence ranks by constructing a hierarchy of master equations, including vertex operators that upgrade or downgrade the coherence rank, as a prelude to a diagrammatic method for calculating continuous-wave spectra. This hierarchy is compared with prevalent Agarwal-type master equations, based on the Dicke pseudospin method, and used in the study of two-level atoms.
We address the microscopic derivation of a quantum master equation in Lindblad form for the dynamics of a massive test particle with internal degrees of freedom, interacting through collisions with a background ideal gas. When either internal or center-of-mass degrees of freedom can be treated classically, previously established equations are obtained as special cases. If in an interferometric setup the internal degrees of freedom are not detected at the output, the equation can be recast in the form of a generalized Lindblad structure, which describes non-Markovian effects. The effect of internal degrees of freedom on center-of-mass decoherence is considered in this framework.