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arXiv:1209.3244 · Canadian Journal of Physics

Phonon laser effect and Dicke–Hepp–Lieb superradiant phase transition in magnetic cantilever coupled to a Bose–Einstein condensate

Aranya B. Bhattacherjee, Tobias Brandes

Published May 16, 2013• 3 citations
arXivHTMLPDF

Abstract

We propose the possibility of a phonon laser by coupling a Bose–Einstein condensate to a nanomechanical cantilever with a magnetic tip. Due to the magnetic coupling, atomic spin flips induce cantilever motion, which can be used to produce a phonon laser. The system is described by the equivalent of the Jaynes–Cummings Hamiltonian. By controlling the number of atoms and the population inversion, one can obtain either a continuous wave or transient lasing. The two-body atom–atom interaction is also shown to coherently manipulate the lasing process. We also show that in the strong coupling limit, the same system can undergo a Dicke–Hepp–Lieb superradiant phase transition. Exotic phase diagrams can be obtained by tuning the two body atom–atom interaction.

DOI
10.1139/cjp-2013-0113

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We propose the possibility of a phonon laser by coupling a Bose–Einstein condensate to a nanomechanical cantilever with a magnetic tip. Due to the magnetic coupling, atomic spin flips induce cantilever motion, which can be used to produce a phonon laser. The system is described by the equivalent of the Jaynes–Cummings Hamiltonian. By controlling the number of atoms and the population inversion, one can obtain either a continuous wave or transient lasing. The two-body atom–atom interaction is also shown to coherently manipulate the lasing process. We also show that in the strong coupling limit, the same system can undergo a Dicke–Hepp–Lieb superradiant phase transition. Exotic phase diagrams can be obtained by tuning the two body atom–atom interaction.
We theoretically study the coupling of Bose-Einstein condensed atoms to the mechanical oscillations of a nanoscale cantilever with a magnetic tip. This is an experimentally viable hybrid quantum system which allows one to explore the interface of quantum optics and condensed matter physics. We propose an experiment where easily detectable atomic spin flips are induced by the cantilever motion. This can be used to probe thermal oscillations of the cantilever with the atoms. At low cantilever temperatures, as realized in recent experiments, the backaction of the atoms onto the cantilever is significant and the system represents a mechanical analog of cavity quantum electrodynamics. With high but realistic cantilever quality factors, the strong coupling regime can be reached, either with single atoms or collectively with Bose-Einstein condensates. We discuss an implementation on an atom chip.
An extended Dicke model, which includes atom-atom interactions and a driving classical laser field, is established for a Bose-Einstein condensate inside an ultrahigh-finesse optical cavity. A feasible experimental setup with a strong atom-field coupling is proposed, where most parameters are easily controllable and thus the predicted a second-order superradiant-normal phase transition may be detected by measuring the ground-state atomic population. More intriguingly, second-order phase transition from the superradiant phase to the ``Mott'' phase is also revealed. In addition, a rich and exotic phase diagram is presented.
This work investigates different coupling mechanisms between ultracold atoms and mechanical oscillators. In a first experiment, atom-surface force is used to couple the vibrations of a mechanical cantilever to the motion of a Bose-Einstein condensate in a magnetic microtrap on a chip. The atoms are trapped at sub-micrometer distance from the cantilever surface. Coupling is used to read out the cantilever vibrations with the atoms. Coupling via surface forces could be employed to couple atoms to molecular-scale oscillators such as carbon nanotubes. In a second experiment, coupling via a 1D optical lattice that is formed by a laser beam retroreflected from the cantilever tip. The optical lattice serves as a transfer rod which couples vibrations of the cantilever to the atoms and vice versa.
Abstract A proposal for simulating the Dicke-Lattice model in a mechanics-controlled hybrid quantum system is studied here. An array of coupled mechanical resonators (MRs) can homogeneously interact with a group of trapped Bose–Einstein condensates (BECs) via the gradient magnetic field induced by the oscillating resonators. Assisted by the classical dichromatic radio-wave fields, each subsystem with the BEC-MR interaction can mimic the Dicke type spin-phonon interaction, and the whole system is therefore extended to a lattice of Dicke models with the additional adjacent phonon-phonon hopping couplings. In view of this lattice model with the Z 2 symmetry, its quantum phase transitions behavior can be controlled by this periodic phonon-phonon interactions in the momentum space. This investigation may be considered as a fresh attempt on manipulating the critical behaviors of the collective spins through the external mechanical method.
Atom lasers have been demonstrated in both pulsed and semi-continuous modes. The dynamics of these devices is predicted to be dramatically different to the optical laser due to fundamental differences between the two types of boson fields, however to date it is the similarities that have been emphasized. Here we show how the atom laser dynamics are strongly affected by coupling of the output beam back to the condensate. Typically research in the field of Bose-Einstein condensation (BEC) 1 relates to studies of fundamental properties, such as collective modes 2 or to the response of the BEC to external stimuli 3. In contrast, the atom laser is one of the most promising technologies to arise from BEC, being the di-rect atomic equivalent of the optical laser 4. Mewes et al. 5 demonstrated the first atom laser, based on the application of pulsed radio-frequency (RF) fields to induce controlled spin flips from magnetically trapped to un-trapped states of a Bose-Einstein condensate. Later it was shown by Hagley et al. 6 that a pulsed Raman out-coupling could be used to achieve a quasi-continuous multi-state atomic beam. Bloch et al. 7 achieved con-tinuous RF out-coulping for up to 100ms, producing a single state atom laser beam, and showed that this beam could be coherently manipulated in direct analogy to the optical laser 8. These experiments, and others 9,10, have conclusively demonstrated that the outcoupling process can be made coherent. They have also demonstrated a number of other similarities be-tween the optical and atomic lasers such as high flux and low divergence of the output beam. In all these works, the similarities between the two sys-tems have been emphasized, however, ultimately it is the differences such as mass and wavelength that will lead to applications of the atom laser. 1