Atomic Pair-State Interferometer: Controlling and Measuring an Interaction-Induced Phase Shift in Rydberg-Atom Pairs

We present experiments measuring an interaction-induced phase shift of Rydberg atoms at Stark-tuned Förster resonances. The phase shift features a dispersive shape around the resonance, showing that the interaction strength and sign can be tuned coherently. We use a pair-state interferometer to measure the phase shift. Although the coupling between pair states is coherent on the time scale of the experiment, a loss of visibility occurs as a pair-state interferometer involves three simultaneously interfering paths and only one of them is phase shifted by the mutual interaction. Despite additional dephasing mechanisms, a pulsed Förster coupling sequence allows for observation of coherent dynamics around the Förster resonance.

Popular Summary

Rydberg atoms are atoms in which one or more electrons are excited to high atomic orbits. In addition to being one of the workhorses of atomic and optical physics, Rydberg atoms have recently become a favored candidate for neutral-atom-based quantum information processing, serving both as single qubits and as components of basic quantum logical gates where coherent control of the phases of the Rydberg atoms becomes essential. This applicability originated in the fact that the interaction between two Rydberg atoms can be turned on and off with a strength contrast of many orders of magnitude by varying their distance. In this experimental paper, we add a new and promising tool for controlling the strength and character of the two-atom interaction, and in turn, shifting the quantum phases of the atoms, by exploiting the Förster resonant energy transfer between the atoms and tuning the resonance with small electric fields (Stark tuning).

The Förster resonant energy transfer occurs between two Rydberg atoms when they are at the right distance and in the right states. An easy way to understand the effect qualitatively in this context is to see the two atoms as two oscillating dipoles that interact with each other. And this interaction can be tuned by a small applied electric field. We start with a cloud of ultracold rubidium atoms and optically excite the atoms to one of their Rydberg states. By applying a small static electric field and increasing its strength gradually, we can make the Rydberg atoms interact with each other more strongly. The field-dependent, and distance-dependent, interaction between two atoms either flips the states of the atoms to different ones or shifts the phase of the original pair state coherently. A tailored laser-pulse sequence allows us to map the coherent evolution of the interaction effects onto the number of Rydberg atoms, which can then be easily detected.

Our proof-of-concept demonstration of a coherently controlled quantum phase shift in Rydberg atoms could open a new possibility for developing quantum phase gates and stimulate further advances in neutral-atom-based quantum information processing.

Figure 1

(a) Schematic of the pair-state interferometer. Interactions between Rydberg atoms change the phase $\phi (U)$ of the $|rr⟩$ state relative to the other states and create population in $|r^{\prime }{r}^{\prime \prime }⟩$. A pulsed Ramsey field couples three states simultaneously. A Rydberg detector detects the number of Rydberg atoms $N_{\mathrm{Ryd}}$, resulting in (b) a Ramsey spectrum (blue data points) depending on the combined detuning $\Delta$ of the two-photon excitation. The red line is a fit to the data. (c) The transfer function for $0.6\pi$-Ramsey pulses describing the dependence of the fitted phase of the Ramsey fringes $\varphi$ on the phase shift $\phi$ in the $|rr⟩$ path for small angles.

Figure 2

(a) Stark map of the relevant pair states (see text). (b) A magnification of the Stark map at the electric fields where the pair states are tuned into resonance. The dotted lines denote the pair-state energies without coupling; the solid lines include the dipole-dipole coupling for an interatomic distance of $9\mu \mathrm{m}$. The energy differences at the resonant electric field $E_{\mathrm{res}}$ and at a detuned electric field $E_{\det }$ are indicated.

Figure 3

(a) Oscillations in the visibility are measured for (b) the pulse sequence of the double-Ramsey experiment. The electric field during the delay time $E_{\det }$ is indicated by the solid horizontal black lines in (a). The oscillations in the visibility (data points with error bars resulting from the standard deviation of the fit to the Ramsey spectrum) are centered around the applied electric field. The solid curves are sinusoidal fits to the data. Blue data (lower three measurements) and red data (upper three measurements) indicate positive and negative Förster defects, respectively. The dotted line indicates the position of the Förster resonance.

Figure 4

Measured frequency $\nu$ of the oscillation in the visibility (data points) versus the calculated Förster defect. The error bars are the standard deviation of the sinusoidal fits. The solid line shows $\nu =|\Delta |$.

Figure 5

Visibility and phase obtained from fits to (a) the measured and (b) the simulated Ramsey spectra versus the electric field. Note that the experimental spectra are plotted versus the calibrated component of the electric field $E_z$ and the simulated data versus the total electric field $|\overrightarrow{E}|$. The uppermost panels show the visibility, the middle panel shows the phase of the Ramsey fringes (solid line) and a quadratic fit to the data (dotted line), and the lower panels show the difference of the measured phase from the pure quadratic behavior. Some example error bars are plotted, denoting the standard deviation of the fit parameter.