Transfer of Phase Information between Microwave and Optical Fields via an Electron Spin

We demonstrate the coherent coupling and the resulting transfer of phase information between microwave and optical fields in a single nitrogen vacancy center in diamond. The relative phase of two microwave fields is encoded in a coherent superposition spin state. This phase information is then retrieved with a pair of optical fields. A related process is also used for the transfer of phase information from optical to microwave fields. These studies show the essential role of dark states, including optical pumping into the dark states, in the coherent microwave-optical coupling and open the door to the full quantum state transfer between microwave and optical fields in a solid-state spin ensemble.

Figure 1

(a) Two microwave fields, with a relative phase, ${\phi }_{\mathrm{mw}}={\phi }_{+}-{\phi }_{-}$, couple resonantly to the $m_s=0$ to $m_s=\pm 1$ transitions and generate a coherent superposition of the $m_s=\pm 1$ states, effectively mapping ${\phi }_{\mathrm{mw}}$ to the phase of the spin coherence. (b) Two optical fields, with relative phase, ${\varphi }_{\text{opt}}={\varphi }_{+}-{\varphi }_{-}$, couple resonantly to the $m_s=\pm 1$ to $A_2$ transitions. The fluorescence from the $A_2$ state features sinusoidal oscillations as a function of ${\varphi }_{\text{opt}}-{\phi }_{\mathrm{mw}}$, effectively reading out the relative microwave phase and transferring the phase information from the microwave to the optical fields.

Figure 2

(a) Pulse sequence for the transfer of phase information from microwave to optical fields. A NV is initialized in the $m_s=0$ state with an $8\mu \mathrm{s}$ green laser pulse. The two MW pulses prepare the NV in a superposition of $m_s=\pm 1$ states. The Raman-resonant optical pulse pair then retrieves the phase information of the superposition spin state. (b) Fluorescence from state $A_2$ detected during the initial 28 ns as a function of relative optical phase. The solid curve is a least-square fit to a sinusoidal oscillation with a period $2\pi$, with the peak normalized to 1. (c) Fluorescence from state $A_2$ as a function of time. The upper (lower) curves are obtained with ${\varphi }_{\text{opt}}$ near a maximum (minimum) of the oscillations in (b). (d) Visibility of the sinusoidal oscillations as a function of fluorescence detection time, derived from experiments similar to those shown in (b). The solid line shows the results of a numerical fit using the decay time derived from the time-resolved fluorescences.

Figure 3

(a) Fluorescence from state $A_2$ as a function of the detuning between two applied optical fields, showing the spectral response for $CPT$. The solid line shows a least-square fit of the dip to an inverted Lorentzian, with a linewidth of 2.8 MHz and with the baseline normalized to 1. (b) Fluorescence from $A_2$ as a function of time. The upper (lower) curve is obtained when the optical detuning satisfies (is 20 MHz away from) the Raman resonance. The solid lines show least-square fits to exponentials, with a decay time of 450 ns for the upper curve. Two decay times, 31 ns and 450 ns, are used for the lower curve.

Figure 4

(a) Pulse sequence for the transfer of phase information from optical to microwave fields. Following an initialization green laser pulse, a MW $\pi$ pulse puts the NV in the $m_s=-1$ state. The Raman resonant optical pulse pair then prepares the NV in a dark state. A pair of MW pulses read-out the phase of the dark state by driving the NV from the dark state to the $m_s=0$ state. Population in state $m_s=0$ is detected via a resonant excitation to the $E_y$ excited state. (b) Fluorescence from state $E_y$ as a function of relative microwave phase. The solid curve is a least-square fit to a sinusoidal oscillation with period $2\pi$ and with the peak normalized to 1. (c) Visibility of the sinusoidal oscillations as a function of the delay between optical-encoding and microwave-readout pulses. The solid line shows a least-square fit to an exponential with a decay time of $0.6\mu \mathrm{s}$.