Dressed dense atomic gases

The interaction between atomic transition dipoles and photons leads to the formation of many-body states with collective dissipation and long-ranged interactions. Here, we put forward and explore a scenario in which a dense atomic gas—where the separation of the atoms is comparable to the transition wavelength—is weakly excited by an off-resonant laser field. We develop the theory for describing such a dressed many-body ensemble and show that collective excitations are responsible for the emergence of many-body interactions, i.e., effective potentials that cannot be represented as a sum of binary terms. We illustrate how collective effects may be probed experimentally through microwave spectroscopy. We analyze time-dependent line shifts, which are sensitive to the phase pattern of the dressing laser, and show that the strong interactions lead to a dramatic slowdown of the relaxation dynamics. Our study provides a so far little explored perspective on dense atomic ensembles interacting with light and promotes this platform as a setting for the exploration of dissipative nonequilibrium many-body physics.

Figure 1

Dressed atomic gas. (a) Sketch of the single-atom level structure. The off-resonant dressing laser (Rabi frequency $\mathrm{\Omega }$, detuning $\mathrm{\Delta }$) weakly drives the transition $\left|1\right.〉\to \left|2\right.〉$ that has a decay rate $\gamma$. The resulting level shifts can be probed via microwave (MW) spectroscopy on the $\left|0\right.〉\to \left|1\right.〉$ transition (Rabi frequency ${\mathrm{\Omega }}_{\mathrm{MW}}$, detuning ${\mathrm{\Delta }}_{\mathrm{MW}}$). (b) Atoms exchange (virtual) photons on the transition $\left|1\right.〉\to \left|2\right.〉$, which lead to the formation of delocalized many-body states (collective excitations) with collective decay rates. Sketched are the collective energy levels for two different atomic configurations $\left|\mathcal{C}\right.〉$ and $\left|{\mathcal{C}}^{\prime }\right.〉$. The many-body level structure depends on the number and spatial arrangement of atoms in the state $\left|1\right.〉$, and the energies of the collective excitation states are shifted and broadened with respect to the single-atom state. The MW field effectuates transitions between the states $\left|\mathcal{C}\right.〉$ and $\left|{\mathcal{C}}^{\prime }\right.〉$ at a rate ${\mathrm{\Gamma }}_{\mathcal{C}\to {\mathcal{C}}^{\prime }}$, permitting a spectroscopic analysis of the dressed-state manifold.

Figure 2

Few-body interactions. Three atoms on an equilateral triangle addressed by a laser with uniform Rabi frequency, $\mathrm{\Omega }=5\gamma$, and detuning $\mathrm{\Delta }=100\gamma$. The atomic dipole moment is pointing in the $z$ direction, perpendicular to the atomic plane. The right panel shows the single-, two-, and three-body contribution ${\varepsilon }_n$ to the (interaction) energy.

Figure 3

MW spectroscopy. (a) One-dimensional chain of atoms with spacing $a$. The atomic transition dipoles are pointing into the $z$ direction, and the laser is either irradiated perpendicular or parallel to the chain. (b) Short-time evolution of the excitation density (upper row) and the MW absorption rate (lower row) for various values of the lattice spacing $ka$ and the MW detuning ${\mathrm{\Delta }}_{\mathrm{MW}}$. The black dotted line indicates the position of the maximum (peak) value at a given time. The laser parameters are $\mathrm{\Delta }=50\gamma$ and $\mathrm{\Omega }=5\gamma$ with the laser being irradiated perpendicular to the chain of $N=40$ atoms. (c) Same as in (b), but with the laser irradiated parallel to the chain. (d) Eigenvalues of the imaginary part of the matrix $\mathbf{M}$ [Eq. (8)] for $N=20$. The colored dots indicate the phase pattern of the atoms in the lowest-energy eigenstate at $ka=\pi$ and $ka=2\pi$, i.e., alternating vs uniform (red and blue mean $\pi$ and zero phase, respectively). (e) Long-time evolution of the excitation density of a resonantly excited chain (${\mathrm{\Delta }}_{\mathrm{MW}}={\mathrm{\Delta }}_{\mathrm{MW}}^0$) of $N=40$ atoms. In the noninteracting limit ($ka\to \infty$) the approach to the steady state follows an exponential with time constant $\tau =\frac{1}{4}{(\mathrm{\Omega }/\mathrm{\Delta })}^2\left(\gamma /{\mathrm{\Omega }}_{\mathrm{MW}}^2\right)$. For a dense gas ($ka=\pi /4$) relaxation slows down dramatically and the time dependence of the density follows a power law. (f) Typical trajectories [white (black): atom in state $\left|0\right.〉$ ($\left|1\right.〉$)] are distinctively different in the two regimes. The noninteracting one is without structure, while in the interacting case collective effects manifest in heterogeneous dynamics. Here, relaxation timescales are nonuniform and may vary drastically in different space-time regions. Examples for regions featuring fast (slow) relaxation are marked in blue (red).