Bose-Einstein condensation and many-body localization of rotational excitations of polar molecules following a microwave pulse

Abstract

We study theoretically the collective dynamics of rotational excitations of polar molecules loaded into an optical lattice in two dimensions. These excitations behave as hard-core bosons with a relativistic energy dispersion arising from the dipolar coupling between molecules. This has interesting consequences for the collective many-body phases. The rotational excitations can form a Bose-Einstein condensate at non-zero temperature, manifesting itself as a divergent T2 coherence time of the rotational transition even in the presence of inhomogeneous broadening. The dynamical evolution of a dense gas of rotational excitations shows regimes of non-ergodicity, characteristic of many-body localization and localization protected quantum order. 72.15.Rn The ability to create and control gases of cold polar molecules has sparked great interest in the quantum manybody physics associated with long-range and anisotropic dipolar interactions [1][2][3][4][5][6][7][8]. These systems open up possibilities to create and to probe interesting many-body phases involving the positional and/or rotational degrees of freedom of the molecules [9]. For polar molecules loaded into deep optical lattices -with positional motion frozen out -the rotational excitations can be used to emulate interesting forms of quantum magnet [10][11][12][13][14][15][16][17][18][19][20][21][22]. Recent experiments [23] have shown evidence of the dipole-dipole interactions between molecules in different lattice sites, which appear as an additional source of decoherence of rotational excitations [23,24].In this paper, we study the many-body physics of the rotational excitations of polar molecules in a two-dimensional (2D) system. We show that in regimes of weak disorder, rather than causing decoherence [23,24], the dipole-dipole interactions can in fact stabilize the coherence up to arbitrarily long times. This stability of coherence arises from the formation of a collective many-body phase with true long-range order. The essential physics arises from the power-law (1/r 3 ) form of dipolar interactions between molecules. This coupling causes the rotational excitations to behave as a gas of (hardcore) bosons with a relativistic dispersion δ k ∝ |k| at small wavevector k. In contrast to massive particles (δ k ∝ |k| 2 ) this relativistic dispersion allows a Bose-Einstein Condensate (BEC) to exist in 2D at non-zero temperature. We show that the formation of this BEC phase leads to a resistance to decoherence of the rotational excitations formed by a microwave pulse, even in the presence of inhomogeneities that would broaden the rotational transition for uncoupled molecules. For very strong inhomogeneous broadening there is a phase transition into an uncondensed phase for which the initial coherence decays exponentially in time.An important feature of the rotational excitations of polar molecules is that they are effectively isolated from any external heat bath. In the presence of disorder such systems are natural candidates to show many-body localization and ...

Synchronization transition in dipole-coupled two-level systems with positional disorder

“…The synchronization transition proposed in Ref. 7 arises in a closed quantum system (under unitary time evolution and conserved energy) so is distinct from synchronization phenomena in driven open quantum systems [8] or in classical models of driven dissipative XY systems [9,10].…”

“…Note, however, that the specific physical setting could lead to variants of this model -in dimensions other than D = 2, or including local frequency offsets (random fields that couple to s z i ), or additional s z i s z j interactions [25] -which could lead to differences in the qualitative physics that we describe. Our primary motivation has been to understand the coupled rotational excitations of polar molecules confined to the sites of an optical lattice [26], for which this model emerges naturally [7]. In that case, we can take |s z = −1/2 to represent the ro-vibrational ground state, | = 0, m = 0 , of the polar molecule at site i and |s z = +1/2 the | = 1, m = 0 rotationally excited state ( is the molecular angular momentum and m its projection perpendicular to the 2D plane).…”

“…These features can be understood using intuition based on the thermodynamic phases of hard-core bosons, representing the s = 1/2 quantum spins in a particle-like picture [7]. Within this picture, the XY spin-spin coupling leads to inter-site hopping of the bosons, which has interesting features for dipolar interactions in 2D.…”

“…To describe this situation requires one to go beyond the simple mean-field models used in Ref. 7. We do so by developing a self-consistent mean-field theory involving an RPA-like decoupling of correlation functions.…”

“…In terms of spins, the BEC of hardcore bosons of Ref. 7 can be viewed as a collectively ordered spin state, with long-range spin-spin correlations. This long-range ordering of the spins translates to a synchronized, phase-locked, oscillation of widely-separated two-level systems.…”