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arXiv:1601.06413 · New Journal of Physics

Collectively induced many-vortices topology via rotatory Dicke quantum phase transition

Priyam Das, Mehmet Emre Tasgin, Özgür Esat Müstecaplıoğlu

Published Sep 9, 2016• 9 citations
arXivHTMLPDF

Abstract

We examine the superradiance of a Bose–Einstein condensate pumped with a Laguerre–Gaussian laser of high winding number, e.g., . The laser beam transfers its orbital angular momentum (OAM) to the condensate at once due to the collectivity of the superradiance. An ℓ -fold rotational symmetric structure emerges with the rotatory superradiance. ℓ number of single-charge vortices appear at the arms of this structure. Even though the pump and the condensate profiles initially have cylindrical symmetry, we observe that it is broken to ℓ -fold rotational symmetry at the superradiance. Breaking of the cylindrical symmetry into the ℓ -fold symmetry and OAM transfer to the condensate become significant after the same critical pump strength. Reorganization of the condensate resembles the ordering in the experiment by Esslinger and colleagues (2010 Nature 264 1301). We numerically verify that the critical point for the onset of the reorganization, as well as the properties of the emitted pulse, conform to the characteristics of superradiant quantum phase transition.

DOI
10.1088/1367-2630/18/9/093022

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We examine the superradiance of a Bose–Einstein condensate pumped with a Laguerre–Gaussian laser of high winding number, e.g., . The laser beam transfers its orbital angular momentum (OAM) to the condensate at once due to the collectivity of the superradiance. An ℓ -fold rotational symmetric structure emerges with the rotatory superradiance. ℓ number of single-charge vortices appear at the arms of this structure. Even though the pump and the condensate profiles initially have cylindrical symmetry, we observe that it is broken to ℓ -fold rotational symmetry at the superradiance. Breaking of the cylindrical symmetry into the ℓ -fold symmetry and OAM transfer to the condensate become significant after the same critical pump strength. Reorganization of the condensate resembles the ordering in the experiment by Esslinger and colleagues (2010 Nature 264 1301). We numerically verify that the critical point for the onset of the reorganization, as well as the properties of the emitted pulse, conform to the characteristics of superradiant quantum phase transition.
We present a theoretical study of the collective excitations of the supersolid annular stripe phase of a spin-orbital-angular-momentum-coupled (SOAM-coupled) spin-1 Bose-Einstein condensate. The annular stripe phase simultaneously breaks two continuous symmetries, namely rotational and U(1)U(1)U(1) gauge symmetry, and is more probable in the condensates with a larger orbital angular momentum transfer imparted by a pair of Laguerre-Gaussian beams than what has been considered in the recent experiments. Accordingly, we consider a SOAM-coupled spin-1 condensate with a $4\ensuremath{\hbar}$ orbital angular momentum transferred by the lasers. Depending on the values of the Raman coupling strength and quadratic Zeeman term, the condensate with realistic antiferromagnetic interactions supports three ground-state phases: the annular stripe, the vortex necklace, and the zero angular momentum phase. We numerically calculate the collective excitations of the condensate as a function of coupling and quadratic Zeeman field strengths for a fixed ratio of spin-dependent and spin-independent interaction strengths. At low Raman coupling strengths, we observe a direct transition from the zero angular momentum to the annular stripe phase, characterized by the softening of a double symmetric roton mode, which serves as a precursor to supersolidity.
The appearance of quantized vortices in a superfluid and a Bose-Einstein condensate (BEC) stems from their nontrivial response to time-reversal symmetry (TRS). Here, we show that breaking of the TRS by, for example, rotation or an external synthetic magnetic field in a transversely driven BEC coupled to a single mode of an optical cavity modifies drastically Dicke superradiance and self-ordering phenomena in this system. In particular, photon scattering from the pump laser into the cavity is amplified by rotational motion of the BEC, leading to so-called “rotational superradiance”—in a loose analogy to black-hole physics—with distinct critical scaling properties. In turn, cavity photons mediate long-range, periodic attractive interactions among the vortices, which compete with pairwise logarithmic repulsive vortex interactions and deform the Abrikosov triangular vortex lattice favoring a stripe-like pattern. Remarkably, the rotation of the BEC and the topological properties of the vortex lattice can be monitored nondestructively through the cavity output field.
Abstract In this paper, we have formulated a theory for the microscopic interaction of the asymmetric Laguerre–Gaussian (aLG) beam with the atomic Bose–Einstein condensate (BEC) in a harmonic trap. Here the asymmetry is introduced to an LG beam considering a complex-valued shift in the Cartesian plane keeping the axis of the beam and its vortex states co-axial to the trap axis of the BEC. Due to the inclusion of the asymmetric nature, multiple quantized circulations are generated in the beam. We show how these quantized circulations are transferred to the BEC, resulting in a superposition of matter vortex states. The calculated Rabi frequencies for the dipole as well as quadrupole transitions during the transfer process show distinct variability with the shift parameters of the beam. A significant enhancement of the quadrupole Rabi frequency for higher vorticity states is observed compared to the symmetric single orbital angular momentum (OAM) mode beam at a particular range of the shift parameters. We also demonstrate the variation of superposition of matter vortex states and observe its distinct feature compared to the superposition of the LG modes for different shift parameters. The first order spatial correlation of the superposed states supports this feature and highlights asymmetry in the degree of transverse coherence along orthogonal directions on the surface.
An analysis of superradiant scattering of light by ultracold atoms is presented in which the pump and scattered light consist of hollow counterrotating Laguerre-Gaussian beams possessing orbital angular momentum. It is shown that the interaction between the Laguerre-Gaussian beams and the atoms can give rise to a superradiant instability in which orbital angular momentum is transferred to the atoms and the probe field is amplified. In the case where the atoms constitute a dilute Bose-Einstein condensate (BEC) that is trapped in a one-dimensional ring geometry, the transfer of orbital angular momentum to the BEC during the instability means that the BEC spontaneously develops rotation in the ring.
We investigate the ground-state phase diagram and excitation spectrum of an interacting spinor Bose-Einstein condensate with spin-orbital-angular-momentum (SOAM) coupling realized in recent experiments by introducing atomic Raman transition with a pair of copropagating Laguerre-Gaussian laser beams that carry different orbital angular momenta (OAM) [Chen et al., Phys. Rev. Lett. 121, 113204 (2018) and Zhang et al., Phys. Rev. Lett. 122, 110402 (2019)]. Because of the ground-state degeneracy of the single-particle Hamiltonian at vanishing detuning, several angular-stripe phases, which are the superposition of states with different angular quantum numbers, appear in the phase diagram. However, these phases normally exist at small detuning, which makes them hard to be probed in experiments. We show that for a large OAM difference of the laser beams, an asymmetric kind of angular-stripe phase can exist even at large detuning. The excitation spectra in different phases exhibit distinct features: In the angular-stripe phase there exist two gapless bands corresponding to the broken U(1)\mathrm{U}(1)U(1) and rotational symmetries, while in the half-skyrmion phase the gapless band exhibits a rotonlike structure. Our predictions of the angular-stripe phases and the low-energy excitations can be examined in recently realized Bose-Einstein condensates with SOAM coupling.
The creation of a topological vortex by a superradiant scattering of a Laguerre-Gaussian (LG) beam off an atomic Bose-Einstein condensate (BEC) is theoretically investigated. It is shown that scattered superradiant radiation can be either in a Gaussian mode without angular momentum or in a LG mode with angular momentum. The conditions leading to these two qualitatively distinct regimes of superradiance are determined in terms of the width for the pump laser and the condensate size for the limiting cases where the recoil energy is both much smaller and larger than the atomic interaction energy.