Quantum phase transition of nonlinear light in the finite size Dicke Hamiltonian

B. M. Rodríguez-Lara; Ray-Kuang Lee

doi:10.1364/JOSAB.27.002443

Journal of the Optical Society of America B
Vol. 27,
Issue 11,
pp. 2443-2450
(2010)
•https://doi.org/10.1364/JOSAB.27.002443

Quantum phase transition of nonlinear light in the finite size Dicke Hamiltonian

B. M. Rodríguez-Lara and Ray-Kuang Lee

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B. M. Rodríguez-Lara and Ray-Kuang Lee, "Quantum phase transition of nonlinear light in the finite size Dicke Hamiltonian," J. Opt. Soc. Am. B 27, 2443-2450 (2010)

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Table of Contents Category
- Quantum Optics
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Quantum optics (270.0270)
- Quantum electrodynamics (270.5580)
- Quantum information and processing (270.5585)

About this Article
History
- Original Manuscript: August 10, 2010
- Revised Manuscript: September 14, 2010
- Manuscript Accepted: September 17, 2010
- Published: October 29, 2010

Abstract

We study the quantum phase transition of an N two-level system ensemble interacting with an optical degenerate parametric process, which can be described by the finite size Dicke Hamiltonian plus counter-rotating and quadratic field terms. Analytical closed forms of the critical coupling value and their corresponding separable ground states are derived in the weak and strong coupling regimes. The existence of bipartite entanglement between the two-level system ensemble and photon field as well as between ensemble components for moderate coupling is shown through numerical analysis. Given a finite size, our results also indicate the co-existence of squeezed fields and squeezed atomic ensembles.

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	2 TLS, Fig. 1e, 1f, 1g, 1h, 1i, 1j, 1k, 1l $λ = 3.323$				5 TLS, Fig. 2e, 2f, 2g, 2h, 2i, 2j, 2k, 2l $λ = 3.019$
	A $κ = 0$	B $κ = 0.3$	C $κ = 2.4$	D $κ = 4.8$	A $κ = 0$	B $κ = 0.3$	C $κ = 2.4$	D $κ = 4.8$
$⟨ \hat{n} ⟩$	22.078	4.590	0.502	0.678	45.528	9.417	0.731	0.707
$⟨ Δ {\hat{n}}^{2} ⟩$	22.084	3.155	1.011	2.135	45.545	6.416	1.153	2.162
$⟨ Δ {\hat{X}}^{2} ⟩$	1.000	0.676	1.824	2.941	1.000	0.676	1.645	2.609
$⟨ Δ {\hat{Y}}^{2} ⟩$	1.000	1.481	0.869	0.355	1.000	1.480	1.087	0.426
$⟨ Δ {\hat{X}}^{2} ⟩ ⟨ Δ {\hat{Y}}^{2} ⟩$	1.000	1.000	1.586	1.045	1.000	1.000	1.789	1.112
$⟨ {\hat{J}}_{x} ⟩$	$- 1.000$	0.000	0.000	0.000	$- 2.499$	2.495	0.000	0.000
$⟨ Δ {\hat{J}}_{x}^{2} ⟩$	0.000	$- 0.052$	0.903	0.756	0.001	0.005	5.630	3.576
$⟨ {\hat{J}}_{y} ⟩$	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
$⟨ Δ {\hat{J}}_{y}^{2} ⟩$	0.5000	0.500	0.392	0.364	1.250	1.250	1.147	0.719
$⟨ {\hat{J}}_{z} ⟩$	$- 0.023$	$- 0.512$	$- 0.466$	$- 0.781$	$- 0.068$	$- 0.153$	$- 0.861$	$- 1.902$
$⟨ Δ {\hat{J}}_{z}^{2} ⟩$	0.500	0.5000	0.487	0.269	1.250	1.246	1.232	0.837
$4 ⟨ Δ {\hat{J}}_{z}^{2} ⟩ ⟨ Δ {\hat{Φ}}^{2} ⟩$	1.000	$1.151 \times 10^{47}$	$7.515 \times 10^{54}$	$5.887 \times 10^{51}$	1.000	1.000	$7.180 \times 10^{38}$	$1.682 \times 10^{41}$

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