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arXiv:1502.04075 · Semiconductor Science and Technology

Field-dependent superradiant quantum phase transition of molecular magnets in microwave cavities

Dimitrije Stepanenko, Mircea Trif, Oleksandr Tsyplyatyev, Daniel Loss

Published Aug 25, 2016• 9 citations
arXivHTMLPDF

Abstract

Abstract We study a superradiant quantum phase transition in the model of triangular molecular magnets coupled to the electric component of a microwave cavity field. The transition occurs when the coupling strength exceeds a critical value, d c , which, in sharp contrast to the standard two-level emitters, can be tuned by an external magnetic field. In addition to emitted radiation, the molecules develop an in-plane electric dipole moment at the transition. We estimate that the transition can be detected in state-of-the-art microwave cavities if their electric field couples to a crystal containing a sufficient number of oriented molecules.

DOI
10.1088/0268-1242/31/9/094003

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Abstract We study a superradiant quantum phase transition in the model of triangular molecular magnets coupled to the electric component of a microwave cavity field. The transition occurs when the coupling strength exceeds a critical value, d c , which, in sharp contrast to the standard two-level emitters, can be tuned by an external magnetic field. In addition to emitted radiation, the molecules develop an in-plane electric dipole moment at the transition. We estimate that the transition can be detected in state-of-the-art microwave cavities if their electric field couples to a crystal containing a sufficient number of oriented molecules.
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We study the superradiant phase transition of an array of Rydberg atoms in a dissipative microwave cavity. Under the interplay of the cavity field and the long-range Rydberg interaction, the steady state of the system exhibits an interaction-enhanced superradiance, with vanishing critical atom-cavity coupling rates at a discrete set of interaction strengths. We find that, while the phenomenon can be analytically understood in the case of a constant all-to-all interaction, the enhanced superradiance persists under typical experimental parameters with spatially dependent interactions, but at modified critical interaction strengths. The diverging susceptibility at these critical points is captured by emergent quantum Rabi models, each of which comprises a pair of collective atomic states with different numbers of atomic excitations. These collective states become degenerate at the critical interaction strengths, resulting in a superradiant phase for an arbitrarily small atom-cavity coupling.
We propose an experimental scheme to realize phase transition from {\it dark superradiance} to conventional superradiance in a microwave cavity coupled to polar molecules. The competition between cavity-mediated infinite-range repulsions and finite-range attractive dipolar interactions stabilizes a variety of exotic quantum phases, including vortex, vortex anti-vortex pairs, and superradiant phase, all emerging without external driving fields. In vortex phase associated with {\it dark superradiance}, cavity remains in vacuum state while profoundly reshaping the condensate's ground-state wave functions. In particular, the spin configuration locally parallel but globally anti-parallel is a direct consequence of competing for two nonlocal interactions. Beyond Dicke paradigm, dipolar dressing of condensate enables access to an unexplored regime of repulsion-dominated superradiance. A Bogoliubov analysis of low-energy excitation spectrum confirms that the condensate remains stable, avoiding roton-maxon induced collapse even in strongly dipolar regime.
We study the properties of a generalized Dicke-Ising model realized with an array of Rydberg atoms, driven by microwave electric fields and coupled to an optical cavity. As this platform allows for a precisely tunable anisotropy parameter, the model exhibits a rich landscape of phase transitions and critical phenomena, induced by the interplay of rotating-wave, counter-rotating-wave, and Ising interactions. We develop an improved quantum Monte Carlo algorithm based on the stochastic series expansion that explicitly tracks the Fock state of the quantum cavity. In the superradiant (SR) phase, this allows us to determine, through data collapse, the scaling laws of the photon number. We also demonstrate the vanishing of parity symmetry in finite-size simulations and show that the Rydberg blockade leads to a significant suppression of cavity occupation. Notably, stronger quantum fluctuations induced by the counter-rotating wave terms slightly favor the superradiant solid (SRS) phase over the Solid-1/2 state. Finally, we confirm that the SR phase transition and the transition from the Solid-1/2 to the SRS are second-order. In contrast, the transitions from the Solid-1/2 or SRS to the SR phase are both first-order for any value of the normalized anisotropy parameter.
An ultracold gas of heteronuclear alkali-metal dimer molecules with hyperfine structure loaded into a one-dimensional optical lattice is investigated. The hyperfine molecular Hubbard Hamiltonian (HMHH), an effective low-energy lattice Hamiltonian, is derived from first principles. The large permanent electric dipole moment of these molecules gives rise to long-range dipole-dipole forces in a dc electric field and allows for transitions between rotational states in an ac microwave field. Additionally, a strong magnetic field can be used to control the hyperfine degrees of freedom independently of the rotational degrees of freedom. By tuning the angle between the dc electric and magnetic fields and the strength of the ac field, it is possible to control the number of internal states involved in the dynamics as well as the degree of correlation between the spatial and internal degrees of freedom. The HMHH's unique features have direct experimental consequences such as quantum dephasing, tunable complexity, and the dependence of the phase diagram on the molecular state.
The peculiarities of coherent spin radiation by magnetic nanomolecules is investigated by means of numerical simulation. The consideration is based on a microscopic Hamiltonian taking into account realistic dipole interactions. Superradiance can be realized only when the molecular sample is coupled to a resonant electric circuit. The feedback mechanism allows for the achievement of a fast spin reversal time and large radiation intensity. The influence on the level of radiation, caused by sample shape and orientation, is analysed. The most powerful coherent radiation is found to occur for an elongated sample directed along the resonator magnetic field.