Rydberg atom arrays as quantum simulators for molecular dynamics

Abstract

Rydberg atoms held in optical tweezer arrays combine vibrational and electronic degrees of freedom which can be coupled and manipulated at a microscopic level. This opens opportunities for the quantum simulation of artificial molecular systems and offers in particular a platform for probing complex vibronic dynamics in controlled settings with increasing complexity. Tailored interatomic interactions and electron-phonon couplings yield handles for designing electronic state manifolds, for studying structural transitions, and for exploring non-classical vibrational states near molecular instabilities. Furthermore, this quantum simulator opens opportunities for testing and quantifying the validity of fundamental concepts, such as the Born-Oppenheimer approximation and quantum corrections to it.

Figures (3)

• Figure 1: Atom tweezer arrays and electronic state space. (a) Dumbbell-shaped atom array. Atoms are modeled by a two-level system with states $\ket*{\downarrow}$ (ground state) and $\ket*{\uparrow}$ (Rydberg state). Transitions are driven by a laser with detuning $\Delta$ and Rabi frequency $\Omega$. The tweezer confinement is modelled by a harmonic oscillator with trapping frequency $\omega$ and phonon annihilation operators $a^{(k)}_j$ for the directions $j=x,y,z$. The superscript $k$ labels the atom in the array. The atomic equilibrium positions of the dumbbell are $\bm{r}^{(1)}_0=d(1,0,0)^\mathrm{T}$ and $\bm{r}^{(2)}_0=d(0,0,0)^\mathrm{T}$. (b) Triangular atom array, obtained by extending the dumbbell with a third atom at position $\bm{r}^{(3)}_0=d(1\slash{2},\sqrt{3}\slash{2},0)^\mathrm{T}$. If atom $2$ is in its Rydberg state, the Rydberg state of atom $1$ experiences the interaction energy shift $V(d)$. When the laser detuning cancels this interaction shift, $\Delta=-V(d)$, atom $1$ undergoes a facilitated excitation. (c) Tetrahedral atom array, obtained from the triangle [see (b)] by adding an atom at position $\bm{r}^{(4)}_0=d(1\slash{2},1\slash(2\sqrt{3}),\sqrt{2\slash{3}}) ^\mathrm{T}$. The position $\bm{r}^{(k)}=\bm{r}^{(k)}_0+\delta\bm{r}^{(k)}$ of the $k$-th atom in the array is the sum of the equilibrium position $\bm{r}^{(k)}_0$ and the displacement vector $\delta\bm{r}^{(k)}$, with components $\delta{r}^{(k)}_j=x_0(a^{(k)}_j+(a^{(k)}_j)^\dagger)\slash \sqrt{2}$. (d,e) Visualization of coupled (at rate $\Omega$) resonant electronic states of the tetrahedron. The graph in (d) emerges when choosing the facilitation condition $\Delta=-V(d)$, and (e) is obtained when setting $\Delta=-3V(d)$.
• Figure 2: Energy spectrum and Wigner distribution. (a,b) Energy spectrum (black) of the dumbbell [Fig. \ref{['fig:arrays']}] as a function of the Rabi frequency $\Omega$. The spectrum is computed by exact diagonalization of Eq. \ref{['eq:dumbbellHamiltonian']} with $\kappa=0.1\omega$ and truncating at 100 phonons. In blue, we highlight the ground state. As a reference we show the uncoupled ($\kappa=\xi=0$) spectrum (red). (c,d) Wigner quasiprobability distribution of the ground state of the tetrahedron [Fig. \ref{['fig:arrays']}], Eq. \ref{['eq:wignerDistribution']}, for different values of $\kappa$. We choose $\xi=2\omega$ and $\nu=0.1$. In the top right the squeezing strengths (variance of the position quadrature associated to the mode with annihilation operator $b^{\perp,1}_{\ket*{\uparrow\uparrow\downarrow\downarrow}}$ normalized to the variance for $\kappa=\xi=0$) are shown.
• Figure 3: Potential energy surfaces and ground state energy. (a) Ground state potential energy surface for the triangle shown in Fig. \ref{['fig:arrays']}. We plot the surface in the vicinity of one of the three-fold degenerate minima; the one that is associated with configurations in the vicinity of the leftmost of the three deformed triangular shapes. For $\Omega=0$ this surface is given by Eq. \ref{['eq:potentialEnergySurface']}. The curves shown here are $E_\mathrm{BO}(\Omega;q_{1,\mathrm{min}}(q_2),q_2,q_3=0,q_4=0)$, and the minimum of each curve (see yellow markers) corresponds to the ground state within the boa for a given $\Omega$. At $\Omega=\Omega_\mathrm{c}$ a structural transition between a symmetric and a symmetry-broken triangle takes place (dashed line). For details see the supplemental material supmat. For the electron-phonon coupling parameters we chose $\xi=-0.15\omega$, $\kappa=0.25\omega$, and $\nu=0.1$. (b) Ground state energy of the triangle as a function of the Rabi frequency $\Omega$. The curve $E_{\mathrm{GS},3}$ (blue) is obtained by exact diagonalization (truncated at 20 phonons per mode). The red curve shows the ground state energy $E^\mathrm{BO}_{\mathrm{GS},3}$, obtained in the boa.