We demonstrate a robust single-photon Ramsey interferometer based on a single Rydberg excitation, where the photon is stored as a Rydberg polariton in an ensemble of atoms. This coherent conversion of the photon to Rydberg polariton enables to split an incoming photon into a superposition state of two Rydberg states by applying microwave fields, which constructs two paths of interferometer. Ramsey interference fringes are demonstrated when we scan either the detuning of the microwave or the free evolution time, from which we can obtain the resonant transition frequency of two Rydberg states. We use the Ramsey-like sequence to demonstrate coherent manipulation of the stored single-photon to construct different interference patterns. In addition, the robustness of the Ramsey interferometer to the fluctuation of incoming photon numbers and optical depth (OD) of the atomic ensemble is tested, showing that the coherent of Ramsey interferometer is preserved for input photon number in a range of R in < 15 and for OD varying from 1.0 to 4.0. The robust interferometer will find its applications in quantum precision measurement.
Abstract Ramsey interferometers using internal electronic or nuclear states find wide applications in science and engineering. We develop a matter wave Ramsey interferometer for trapped motional quantum states exploiting the s- and d-bands of an optical lattice and study it both experimentally and theoretically, identifying the different de-phasing and de-coherence mechanisms. Implementing a band echo technique, employing repeated π-pulses we suppress the de-phasing evolution and significantly increase the coherence time of the trapped state interferometer by one order of magnitude. Thermal fluctuations are the main mechanism for the remaining decay of the contrast. Our demonstration of an echo-Ramsey interferometer with trapped quantum states in an optical lattice has potential application in the study of quantum many-body lattice dynamics, and motional qubits manipulation.
Our work here presents the analytical expressions for a typical Ramsey interferometric sequence for a three- and a five-level system. The analytical expressions are derived starting from the first principals of unitary time evolution operators. We focus on the three- and five-level systems because we propose a novel Ramsey interferometer created by a trapped two-state Bose-Einstein Condensate driven by dipole oscillations and gravitational sag. It involves the
87Rb atoms in states
∣F=2,mF=+2⟩ (∣+2⟩) and
∣F=2,mF=+1⟩ (∣+1⟩) of the
52S21 ground state. Though the interferometer focusses on the two-levels, the experimental readouts involve all the five states in
F=2 hyperfine manifold. Therefore, the analytical derivation was first tested for three-levels and then expanded to five-levels. We developed the expressions for five-levels for greater analytical accuracy of the experimental scenario. This work provides a step-by-step outline for the derivation and methodology for the analytical expressions. These analytical formulae denote the population variation during Rabi and Ramsey oscillations for each state as well as the overall average for both the three- and five-level cases. The expressions are derived within the rotating wave approximation (RWA) under the equal Rabi condition. Further, by following the derivation methodology, these analytical expressions can be easily expanded for Ramsey sequences with unequal pulses, and Ramsey sequences with spin echo techniques.