SUPER and femtosecond spin-conserving coherent excitation of a tin-vacancy color center in diamond

Abstract

The coherent excitation of an optically active spin system is one of the key elements in the engineering of a spin-photon interface. Using the novel SUPER scheme, we coherently control the main optical transition of a tin-vacancy color center in diamond with nonresonant ultrashort optical pulses. Furthermore, we implement a femtosecond control scheme using resonant pulses for achieving record short quantum gates applied to diamond color centers. We simulate the applicability of the SUPER scheme to spin qubits and experimentally investigate spin mixing. Finally, we propose a spin-spin entanglement scheme in a scenario where the excitation with broadband pulses is incompatible with spin-selective excitation. The employed ultrafast quantum gates open up a new regime of quantum control with solid-state color centers, enabling multi-gate operations and efficient spectral filtering of the excitation laser from deterministically prepared coherent photons.

Figures (6)

• Figure 1: The tin-vacancy color center and its optical control.a Energy level manifold of the SnV with and without an applied magnetic field. b Example of population inversion dynamics from ground to excited states, for orbital ($\left|1\right\rangle\rightarrow\left|3\right\rangle$) and spin states ($\tfrac{1}{\sqrt{2}}(\left|1,\downarrow\right\rangle+\left|1,\uparrow\right\rangle)\rightarrow\tfrac{1}{\sqrt{2}}(\left|3,\downarrow\right\rangle+\left|3,\uparrow\right\rangle)$), using resonant or SUPER schemes. c Simplified experimental pulse carving setup. The spectral bands of a broadband pulse are dispersed spatially with the help of a diffraction grating and reflected onto a spatial light modulator (SLM). By defining slits on the pixels of the SLM, it is possible to change the polarization of the desired frequency bands. Undesired frequencies are filtered out at the output with the help of a polarizer. Using the pulse carver it is possible to engineer pulses with different spectral shapes from a broad bandwidth Gaussian pulse. In this work, we use three configurations: i) a resonant single narrowband pulse, ii) resonant semi-broadband quadrilateral-like femtosecond pulse, iii) nonresonant two-color detuned Gaussian narrowband pulse to implement the SUPER scheme. The real pulse spectra employed in the experiment are presented in the Supplementary Fig. \ref{['fig:sup_pulseSpectra']}.
• Figure 2: Coherence measurements and quantum control of the SnV.a Lifetime measurement of the SnV. By applying the narrowband pulse at $\pi$-rotation power and analyzing the fluorescence response, we extract an average spontaneous emission lifetime of 16.2 (6) ns, which corresponds to the $T_1$ of our optical qubit. b Time-resolved Rabi oscillations under a quasi-continuous excitation scheme, where a continuous wave laser is switched on with an acousto-optic modulator, and the fluorescence response is recorded. The observed Rabi oscillations establish the coherence of the investigated qubit. From the amplitude decay of the oscillations, we estimate an overall dephasing of the optical qubit under the experimental conditions as $T_2^*$ = 10.9 (4) ns. c Optical Rabi rotations extracted by varying the power and integrating the total amount of registered photons using a $\sim$40 GHz wide pulse of 15 ps duration. The dashed line indicates a $\pi$-rotation. d Photon purity measurement of the emitter fluorescence at a power calibrated from (c, dashed line) to perform a $\pi$-rotation. The estimated $g^{(2)}(0)$ is 0.1 (1), which confirms the single-photon nature of the collected emission. e Optical Rabi rotations extracted by varying the pulse power and integrating the total amount of registered photons using a 1400 GHz wide quadrilateral broadband pulse with femtosecond duration. The dashed line indicates a $\pi$-rotation. The peak around 4 $\sqrt{\rm pJ}$ corresponds to the 3$\pi$ rotation Inset: Measurement of the pulse duration using an autocorrelator. Full-width-half-maximum of the sech$^2$ autocorrelation signal is multiplied by a factor of 0.647 to deconvolve the pulse duration. f Photon purity measurement of the emitter fluorescence at a power calibrated from (e, dashed line) to perform a $\pi$-rotation. With the estimated $g^{(2)}(0)$ = 0.2 (6), the single-photon emission is confirmed but a higher background contribution compared to narrowband pulses is detected. Horizontal error bars in c and d correspond to the error specified by the powermeter sensor head. The remaining uncertainties in the figure are extracted from the 95% confidence intervals returned by the fit algorithms.
• Figure 3: Implementation of the SUPER scheme.a Experimental data obtained by sending two-color nonresonant pulses while one of the two pulses' (the scan pulse) power and detuning to the SnV resonance is varied. The pulse power of the fixed pulse is set to maximum available (corresponding to approximately $7\pi$), and its detuning to the SnV resonance is set to 117 GHz. The inversion is calculated by taking the ratio of the absolute number of registered counts after applying the two-color SUPER pulse and a resonant narrowband $\pi$-pulse. b Theoretical simulation of the SUPER excitation using the experimental pulse parameters. A good agreement between the experimental data and simulation is observed. c Photon purity measurement conducted to the emission at the maximum emission. $g^{(2)}(0)$ of 0.1 (4) is obtained. This implies a single-photon emission from an individual emitter. Uncertainty is extracted from the confidence interval retrieved from the fit algorithm.
• Figure 4: SUPER applied to spin qubits.a Simulation of the temporal evolution of the ground and excited states of the spin qubit under an optimized magnetic field and SUPER pulses. Population exchange dynamics of $\left|1,\downarrow\right\rangle\rightarrow\left|3,\downarrow\right\rangle$ and $\left|1,\uparrow\right\rangle\rightarrow\left|3,\uparrow\right\rangle$ follow a similar trajectory. b Coherence transfer from the ground state superposition, to the excited state superposition: $|\rho_1, \downarrow \uparrow \!\!| = |\left\langle 1, \downarrow \right| \hat{\rho} \left|1, \uparrow\right\rangle | \rightarrow |\rho_3, \downarrow \uparrow\!\!| = |\left\langle 3, \downarrow \right| \hat{\rho} \left|3, \uparrow\right\rangle|$. c Subsequentially applied spin initialization and readout pulses with a variable delay $\tau$ for estimating spin coherence. The observable peak at $\sim$ 0.13 ms is the fluorescence induced by the applied SUPER excitation. d The thermalization of the spin states when a SUPER pulse is applied. Decay time of the population to the mixed state yields the $T_{\rm 1,spin}$ time. e The control measurement for spin population thermalization when no SUPER pulses are applied between initialization and readout pulses. Uncertainties are extracted from the 95% confidence intervals retrieved from the fit algorithm. f Illustration of the proposed entanglement scheme based on generating photonic qubits encoded in the frequency basis. Two SnVs are first prepared in an equal spin superposition in state. Next, using the SUPER scheme population is inverted to excited state, while maintaining the probability amplitudes of the spin levels. Finally, the two SnVs emit photons with frequencies entangled to their spin-state. Using Hong-Ou-Mandel interference, detecting two clicks on two detectors heralds the state when two photons are distinguishable and the spin states of two SnVs are anti-correlated.
• Figure 5: Pulse block diagram for experiments conducted under zero magnetic field. A trigger signal sent to the time tagger starts the histogram of received counts for the whole sequence. A charge state initialization pulse (blue, 445 nm) ensures the SnV is in its bright state. Finally, a resonant ultrafast pulse or a red detuned pulse pair (for SUPER scheme) excites the emitter, and the subsequent fluorescence signal is measured.