Multipole transitions of Rydberg atoms in modulated ponderomotive potentials

We consider multipole transitions between Rydberg states in amplitude-modulated standing-wave ponderomotive potentials. For experimentally realizable depths of the ponderomotive potential, we find Rabi frequencies of tens of kilohertz. The transitions are not subject to dipole selection rules and allow for changes in the angular momentum quantum number up to about 5. The effects of energy level shifts caused by the ponderomotive potential are discussed.

Figure 1

Ponderomotive optical lattice potential amplitude modulated at frequency $\Omega$ for $\Omega t=0$ (solid) and $\pi$ (dotted) vs the Rydberg-electron coordinate in the center-of-mass frame, $z$, where $z_0$ is the location of the lattice potential peak nearest to the Rydberg-atom center of mass. Equipotential surfaces for the ponderomotive potential are planes perpendicular to the $z$ direction, which is chosen to be the quantization axis.

Figure 2

Rabi frequencies $\mid \chi \mid$ of the transitions $\mid n,l=0,m=0⟩\leftrightarrow \mid n+1,l^{\prime },m=0⟩$ for the indicated values of $l^{\prime }$ vs principal quantum number $n$ and lattice position $z_0$. The underlying amplitude-modulated ponderomotive lattice has a temporal modulation amplitude of $B=\hslash \times {10}^6\mathrm{rad}∕\mathrm{s}$. The Rabi frequencies are displayed on a ten-step linear gray scale ranging from $0\text{to}2.5\times {10}^5\mathrm{rad}∕\mathrm{s}$. (Note that $l^{\prime }={\tilde{l}}_{\min }$ for the cases shown in this figure.)

Figure 3

Maximal Rabi frequencies of the transitions $\mid n,l=2,m=0⟩\leftrightarrow \mid n-1,l^{\prime },m=0⟩$ of Rb Rydberg atoms at the indicated values of $l^{\prime }$ vs principal quantum number $n$. The underlying ponderomotive lattice has an amplitude-modulation parameter of $B=\hslash \times {10}^6\mathrm{rad}∕\mathrm{s}$. The heavy dashed lines delineate the range of the transition frequencies of all transitions in the plot. For $n\sim 50$, all Rabi frequencies are large, and the transition frequencies are in a range that is favorable for experimental studies.

Figure 4

Level shift of the state $\mid nD,m=0⟩$ of Rb in a ponderomotive potential with $A=\hslash \times {10}^6\mathrm{rad}∕\mathrm{s}$ and $B=0$ in Eq. (2). The shift ranges from 0 (white) to $\hslash \times 2\times {10}^6\mathrm{rad}∕\mathrm{s}$ (black) and is displayed on a linear gray scale.

Figure 5

(a) Rabi frequencies for $A=B=\hslash \times {10}^6\mathrm{rad}∕\mathrm{s}$ of the transition $\mid nD,m=0⟩\leftrightarrow \mid (n-1)F,m=0⟩$ of Rb Rydberg atoms on a linear gray scale ranging from 0 (white) to $5\times {10}^5\mathrm{rad}∕\mathrm{s}$ (black). The overlaid lines indicate the frequency shift of the transition induced by the ponderomotive potential (solid, $5\times {10}^3\mathrm{rad}∕\mathrm{s}$; long-dashed, ${10}^4\mathrm{rad}∕\mathrm{s}$; dashed, $2\times {10}^4\mathrm{rad}∕\mathrm{s}$; short-dashed, $4\times {10}^4\mathrm{rad}∕\mathrm{s}$; dotted, $8\times {10}^4\mathrm{rad}∕\mathrm{s}$). The + and − signs indicate the sign of the shift in various domains. (b) Same as (a) for the transition $\mid nD,m=0⟩\leftrightarrow \mid (n-1)G,m=0⟩$.