Optical properties of atomic Mott insulators: From slow light to dynamical Casimir effects

Iacopo Carusotto, Mauro Antezza, Francesco Bariani, Simone De Liberato, and Cristiano Ciuti

Phys. Rev. A 77, 063621 – Published 23 June 2008

Abstract

We theoretically study the optical properties of a gas of ultracold, coherently dressed three-level atoms in a Mott insulator phase of an optical lattice. The vacuum state, the band dispersion and the absorption spectrum of the polariton field can be controlled in real time by varying the amplitude and the frequency of the dressing beam. In the weak dressing regime, the system shows unique ultraslow-light propagation properties without absorption. In the presence of a fast time modulation of the dressing amplitude, we predict a significant emission of photon pairs by parametric amplification of the polaritonic zero-point fluctuations. Quantitative considerations on the experimental observability of such a dynamical Casimir effect are presented for the most promising atomic species and level schemes.

Received 26 November 2007

DOI:https://doi.org/10.1103/PhysRevA.77.063621

Authors & Affiliations

Iacopo Carusotto^1,*, Mauro Antezza¹, Francesco Bariani¹, Simone De Liberato^2,3, and Cristiano Ciuti²

¹CNR-INFM BEC Center and Dipartimento di Fisica, Università di Trento, via Sommarive 14, I-38050 Povo, Italy
²Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Diderot-Paris 7 et CNRS, UMR 7162, 75013 Paris, France
³Laboratoire Pierre Aigrain, École Normale Supérieure, 24 rue Lhomond, 75005 Paris, France

^*carusott@science.unitn.it

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Vol. 77, Iss. 6 — June 2008

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Images

Figure 1
(Color online) Sketch of the level schemes under consideration.Reuse & Permissions
Figure 2
(Color online) Hopfield $u$ and $v$ coefficients (a,b), group velocity (c), and absorption coefficient (d) of the middle polariton (MP) as a function of dressing amplitude $Ω_{C}$ in the resonant $(ω_{e} = {\tilde{ω}}_{m})$ case. On the scale of the figure, the analytical approximations (42, 37, 38, 39, 41) are undistinguishable from the exact calculations. Vertical lines indicate the dressing amplitude values used in the next figures. The system parameters correspond to the $D_{2}$ line of a Mott insulator system of ${}^{87}R b$ atoms with filling factor $n = 1$ in a $a_{L} = 300 nm$ lattice, $\bar{C} / ω_{e} = 1.7 \times 10^{- 4}$ , $λ_{e} = 2 π / k_{e} = 2 π c / ω_{e} = 780 nm$ .Reuse & Permissions
Figure 3
(Color online) Panels (a,c,e): Dispersion relation $ω (k)$ of the three polariton modes. Panels (b,d,f): Corresponding absorption spectrum $κ^{abs}$ as a function of the polariton frequency $ω$ . Same system parameters as in Fig. 2. Black, red, and green lines refer to the lower polariton (LP), the middle polariton (MP), the upper polariton (UP), respectively. The blue dashed line in (a,c,e) is the free photon dispersion $ω = c k$ . Panels (a,b): Resonant $ω_{e} = {\tilde{ω}}_{m}$ , weak dressing $Ω_{C} / \bar{C} = 1.86 \times 10^{- 4} ⪡ 1$ case. Insets in (a,b): Magnified views of the most significant parts of the MP branch. Panels (c,d): Resonant $ω_{e} = {\tilde{ω}}_{m}$ , strong dressing $Ω_{C} / \bar{C} = 2$ case. Panels (e,f): Nonresonant ${\tilde{ω}}_{m} - ω_{e} = 5 \bar{C}$ , strong dressing $Ω_{C} / \bar{C} = 2$ case. In the absorption (b,d,f) panels: $Λ$ level scheme with $γ_{e} / 2 π = 6 MHz$ and $γ_{m} / 2 π = 10 Hz$ (solid lines); ladder level scheme with exchanged $γ_{e} / 2 π = 10 Hz$ and $γ_{m} / 2 π = 6 MHz$ values (dotted lines).Reuse & Permissions
Figure 4
(Color online) Sketch of the slab geometry under consideration.Reuse & Permissions
Figure 5
(Color online) Spectrum of the dynamical Casimir emission rate per unit surface and unit solid angle around the normal direction $(θ_{\pm} = 0)$ as a function of the modulation frequency $ω$ for the resonant case $ω_{e} = {\tilde{ω}}_{m}$ , a slab thickness $L_{slab} = 10 μ m$ in the absence of enclosing cavity, and a relative modulation amplitude $δ Ω_{C} / Ω_{C} = 0.05$ . Same system parameters as in Fig. 3. (a) Weak dressing $Ω_{C} / \bar{C} = 1.86 \cdot 10^{- 4} ⪡ 1$ ; (b,c) strong dressing $Ω_{C} / \bar{C} = 2$ . The circles in (a,b,c) are the result of the exact calculation (63). The solid lines in (a,b) are the analytical approximation (52). The red dashed line in (c) is the prediction of the dispersionless, time-varying dielectric model based on Eq. (55). Panels (a,b) correspond to the band dispersion and absorption spectra shown in Figs. 3a, 3b, 3c, 3d. Black, red, and green colors in (a,b) refer to the lower (LP), the middle (MP) and the upper (UP) polaritons, respectively.Reuse & Permissions
Figure 6
(Color online) Prediction (63) for the dynamical Casimir emission rate per unit surface and unit solid angle around the normal direction $(θ_{\pm} = 0)$ as a function of the coupling amplitude $Ω_{C}$ for a fixed value of the relative modulation amplitude $δ Ω_{C} / Ω_{C} = 0.05$ at the fully resonant point $ω / 2 = ω_{e} = {\tilde{ω}}_{m}$ . Same system parameters as in Fig. 5: The magenta circle and the blue diamond correspond to, respectively, the weak (a) and strong (b) dressing regimes.Reuse & Permissions

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