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arXiv:quant-ph/0503015

Exploring super-radiant phase transitions via coherent control of a multi-qubit--cavity system

Timothy Jarrett, Chiu Fan Lee, Neil F. Johnson

Published Mar 1, 2005• 0 citations
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Abstract

We propose the use of coherent control of a multi-qubit--cavity QED system in order to explore novel phase transition phenomena in a general class of multi-qubit--cavity systems. In addition to atomic systems, the associated super-radiant phase transitions should be observable in a variety of solid-state experimental systems, including the technologically important case of interacting quantum dots coupled to an optical cavity mode.

DOI
10.48550/arxiv.quant-ph/0503015

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We propose the use of coherent control of a multi-qubit--cavity QED system in order to explore novel phase transition phenomena in a general class of multi-qubit--cavity systems. In addition to atomic systems, the associated super-radiant phase transitions should be observable in a variety of solid-state experimental systems, including the technologically important case of interacting quantum dots coupled to an optical cavity mode.
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Recent advances in nanostructure fabrication and optical control suggest that it will soon be possible to prepare collections of interacting two-level systems (i.e., qubits) within an optical cavity. Here we show theoretically that such systems could exhibit phase transition phenomena involving spin-glass phases. By contrast with traditional realizations using magnetic solids, these phase transition phenomena are associated with both matter and radiation subsystems. Moreover the various phase transitions should be tunable simply by varying the matter-radiation coupling strength.
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We propose a way to realize a multiqubit tunable phase gate of one qubit simultaneously controlling nnn target qubits with atoms in cavity QED. In this proposal, classical pulses interact with atoms outside a cavity only, thus the experimental challenge of applying a pulse to an intracavity single atom without affecting other atoms in the same cavity is avoided. Because of employing a first-order large detuning, the gate can be performed fast when compared with the use of a second-order large detuning. Furthermore, the gate operation time is independent of the number of qubits. This proposal is quite general and can be applied to various superconducting qubits coupled to a resonator, nitrogen-vacancy centers coupled to a microsphere cavity, or quantum dots in cavity QED.
We review the recent developments and the current status in the field of quantum-gas cavity QED. Since the first experimental demonstration of atomic self-ordering in a system composed of a Bose–Einstein condensate coupled to a quantized electromagnetic mode of a high-Q optical cavity, the field has rapidly evolved over the past decade. The composite quantum-gas-cavity systems offer the opportunity to implement, simulate, and experimentally test fundamental solid-state Hamiltonians, as well as to realize non-equilibrium many-body phenomena beyond conventional condensed-matter scenarios. This hinges on the unique possibility to design and control in open quantum environments photon-induced tunable-range interaction potentials for the atoms using tailored pump lasers and dynamic cavity fields. Notable examples range from Hubbard-like models with long-range interactions exhibiting a lattice-supersolid phase, over emergent magnetic orderings and quasicrystalline symmetries, to the appearance of dynamic gauge potentials and non-equilibrium topological phases. Experiments have managed to load spin-polarized as well as spinful quantum gases into various cavity geometries and engineer versatile tunable-range atomic interactions. This led to the experimental observation of spontaneous discrete and continuous symmetry breaking with the appearance of soft-modes as well as supersolidity, density and spin self-ordering, dynamic spin-orbit coupling, and non-equilibrium dynamical self-ordered phases among others. In addition, quantum-gas-cavity setups offer new platforms for quantum-enhanced measurements. In this review, starting from an introduction to basic models, we pedagogically summarize a broad range of theoretical developments and put them in perspective with the current and near future state-of-art experiments.