Single photonic qutrit in a collective Rydberg polariton

Abstract

We report on the coherent creation, control and read-out of a single photonic qutrit in a Rydberg ensemble. In each measurement, an optical photon is stored as a Rydberg polariton through electromagnetically induced transparency. Employing two microwave fields, the polariton is driven into an arbitrary superposition of three collective states, each encoded in a Rydberg state. The collective state is mapped into a photonic time-bin qutrit with the microwave field and read out sequentially. The complete sequence, including preparation, control, and read-out, is less than 1.8~$μ$s, which mitigates decoherence significantly. We measure the coherence of the qutrit with non-destructive Ramsey interferometry, which is preferable for quantum information processing, and find good quantitative agreement with the theoretical model. The ability to write, process and read out the single photonic qutrit on microsecond time scales with microwave coupled Rydberg states demonstrates the coherent connectivity among the high Hilbert space of the qutrit.Our study is an important step in exploring qutrit based quantum information processes and quantum simulation of topological physics with microwave coupled Rydberg atom ensembles.

Figures (4)

• Figure 1: The setting. (a) The experimental apparatus. A probe and control laser counter-propagate in an ultracold atom ensemble. Atoms are excited from ground state $\vert g\rangle$ to Rydberg state $\vert r_1\rangle$ via an intermediate state $\vert e\rangle$. The relevant atomic levels are shown in (a1). By storing a probe photon in a Rydberg state $\vert r_1\rangle$ as Rydberg polaritons, we employ MW fields to control and manipulate collective Rydberg states that form state vectors of qutrit. An $\mu1$ MW field (Rabi frequency $\Omega_{\mu1}$) drives the transition $\vert {r_1}\rangle\to\vert {r_2}\rangle$. The $\mu2$ MW field (Rabi frequency $\Omega_{\mu2}$) is applied to connect to the third Rydberg state $\vert {r_3}\rangle$. (a2) The measured $g^{(2)}(\tau)$ of the retrieval signal in $\vert r_1\rangle$. (b) Time sequence of a Ramsey interferometer by modulating the $\mu2$-field. A visualisation of this sequence is shown in the supplementary material, based on the 'octant plot' framework festenstein2023arbitrary. (c) Interference fringes as a function of $\Delta_{\mu1}$ with $\Omega_{\mu2}t_{\mu2}=2\pi$ (left) and $3\pi$ (right), respectively. The red dashed line shows a calculation based on Eq. (\ref{['I_0']}). The blue solid line represents results taking into account the dissipation. See text for details.
• Figure 2: Read-out of the qutrit vectors. (a) Timing sequences for performing the control and read-out of qutrit. (b) The read-out of population in states $\vert {R_1}\rangle$ (blue area), $\vert {R_2}\rangle$ (purple area) and $\vert {R_3}\rangle$ (green area) are about 47.1 %, 38.6 % and 14.2 %, respectively. In this experiment, we set $\Omega_{\mu2}t_{\mu2}=2\pi$. (c) The time evolution of the populations in three different Rydberg states for $\Omega_{\mu2} = 2\pi\times12.5$ MHz. Changing time $t_{\mu2}$, populations in $\vert R_2\rangle$ and $\vert R_3\rangle$ oscillate. (d) Population of $\vert {R_\alpha}\rangle$ integrated over the retrieve time. It is shown the Rabi oscillation between states $\vert {R_2}\rangle$ and $\vert {R_3}\rangle$. The solid lines are sinusoidal fittings for guiding eyes.
• Figure 3: Illustrating coherence of the prepared qutrit. (a) Measured Ramsey fringes as a function of both $\Delta_{\mu1}$ and $\Omega_{\mu2}$ with $t_{\mu 2}$ = 250 ns. Each data is normalized to its maximum. (b) Theoretical Ramsey fringes calculated with three-level rotation matrices based on Eq. (\ref{['I_0']}). (c) The measured interference fringes (red dots) as a function of $\Delta_{\mu1}$ with $\Omega_{\mu2}t_{\mu2}=2\pi$. The black solid line shows the theoretical calculation. The red dashed line represents the results with Rydberg interactions.
• Figure 4: Restoring quantum coherence of the qutrit. Data points show the visibility of the Ramsey fringes as a function of the $\Omega_{\mu2}$. The solid line is the theoretical result determined by Eq. (\ref{['visibility']}). An excellent agreement between the experiment and theory can be seen.