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Coherent Manipulation of Electron Spins In an ensemble of Nitrogen Vacancy Centers in Diamond

Chiranjib Mitra�IISER Kolkata

Anuvab Nandi, Samiran Chakraborti, Himadri Himani, Sumit Mukherjee, Sayan Chakraborty, and Chiranjib Mitra

"An oscilloscope based method for pulsed Optically Detected Magnetic Resonance in an ensemble of NV centers in diamond." arXiv:2404.05629 (2024).

National Symposium on Quantum Information and Foundations (NSQIF2025)

ISI Kolkata, February 20-21, 2025

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Outline

Nitrogen Vacancy Centre in Diamond

Optical Detection of Magneto-resonance (ODMR)

Pulsed ODMR and Rabi Oscillations

Spin echo measurements and spin bath

Dynamical Decoupling – reducing the effects of the environment

Conclusions and future work

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Nitrogen Vacancy Centers in Diamond

NV Center Structure [1]

Orbital Arrangement [2]

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Energy Level Diagram

The NV center is a “deep” defect. This leads to enhanced coherence times.
When green laser is excited, the NV centers are excited from the ground state to the phonon sideband above the excited state.
If the NV center was initially in the ms =0 state, it is more likely to decay directly from the excited state to the phonon sideband of the ground state, emitting red photons.
If the NV center was initially in the ms =+-1 state, it is more likely to decay through the singlet state.

Level Structure [1]

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NV-Center Triplet Ground State

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Experimental Setup

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Optically Detected Magnetic Resonance Spectrum (CW)

A magnetic field of 43.62 Gauss was aligned along one of the NV axes with an error of around 4 degrees. We choose the central hyperfine line corresponding to m_s=-1, m_I=0 for further pulsed ODMR investigations.

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General Pulse Sequence

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Oscilloscope Acquisition

An example time trace on the oscilloscope.

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SNR vs Readout Time

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SNR vs Sampling Rate

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Longitudinal relaxation

The longitudinal relaxation time T₁ is primarily affected by spin-phonon interactions, and is found to be in the range of milliseconds.

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Rabi Oscillations

The duration of π/2 pulse is found to be 257.73 ns, and decay rate is 1.175 us.

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Rabi Frequency vs Microwave power

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Rabi Oscillations and its Frequency Domain Results

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Spin Echo - Pulse Sequence

The first π/2 pulse rotates the spin from ms=0 about the y-axis to the x-y plane.

The spins are then allowed to precess freely for a time T dephasing, during which they not only dephase but also decohere.

A π pulse then rotates the dephased spins about the y−axis, following which they are allowed to freely precess again, and they start to rephase. They are allowed to do so for a duration of T rephasing.

The final π/2 pulse rotates the spins from the x-y plane back to z-axis for measurement.

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Spin Echo - Experimental Data

Variation of the contrast with the rephasing time.

Spin echo signal

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Spin Echo - Revival

T_free= free precession period

T_13C= Larmor precession period of 13C nuclei

n = integer

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Dynamical Decoupling Sequence

This sequence corrects for pulse errors in the π pulses.

The sequence is realizing an equivalent high pass filter function which decouples the low frequency noise of the environment from the system and increases effective coherence time.

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Carr Purcell Meiboom Gill (CPMG)

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Understanding Aliasing

With Aliasing

No aliasing

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Effective T2 vs Number of pulses

The effective T2 increased with number of pulses. For 1024 pulses, we got effective T2 of 1.183±0.075 ms.

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Gotz S Uhrig; New Journal of Physics 10, 083024 (2008)

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Dynamical Decoupling as Filter Function problem

The coherence after evolution for time τ is given by

χ(τ) can be written as

The power spectral density is given by

The filter function for the CPMG pulse is given by

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Carr Purcell Meiboom Gill (CPMG)

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Filter Characteristics for CPMG sequence

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References

[1] Zhang, Haimei, et al. "Little bits of diamond: Optically detected magnetic resonance of nitrogen-vacancy centers." American Journal of Physics 86.3 (2018): 225-236.

[2] Avalos, Claudia Esther. Detection and polarization of nuclear and electron spins using nitrogen-vacancy centers. University of California, Berkeley, 2014.

[3] Nandi, Anuvab, et al. "An oscilloscope based method for pulsed Optically Detected Magnetic Resonance in an ensemble of NV centers in diamond." arXiv preprint arXiv:2404.05629 (2024).

[4] Gotz S Uhrig; New Journal of Physics 10, 083024 (2008)

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Acknowledgements

I would like to thank my graduate student Anuvab Nandi for the experimental work.
I would like to thank my undergraduate students involved with the work - Samiran Chakraborti, Himadri Himani, Sayan Chakraborty, Abir Mondal, Yashvardhan Jain.
I would also like to acknowledge my former postdoc Sumit Mukherjee.
I would like to thank DST for funding.

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Conclusions and Future Work

Design of novel microwave devices to achieve better Rabi frequency.
Perform the experiment at low temperatures to get further extension of the coherence time.
Comparison of various dynamical decoupling sequences like CPMG, UDD, XY-8 etc.
Quantum sensing using dynamical decoupling.
Investigation of many-body phenomena like spin lock, discrete-time crystals, and many-body localization in dense ensembles at room and low temperatures.
Ongoing attempt to explain the CPMG data

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Backup Slides

H = \sum_i \omega_i b_i^\dagger b_i + \frac{1}{2} \sigma_z \sum_i \lambda_i (b_i^\dagger + b_i) + E.

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Rotating Frame Dynamics

The free Hamiltonian of our effective two level system is given as

When a microwave field is applied, the Hamiltonian becomes

When we go to a frame which is rotating at ω, and apply the rotating wave approximation, then the Hamiltonian becomes

When ω=ω₀, the z component vanishes and the y component survives.

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Signal and noise vs Readout Time

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Understanding variation in signal and noise

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Dephasing of a qubit

The dynamics of a qubit while dephasing is as follows.

The dynamics of the qubit under this Hamiltonian is given by

In an ensemble average, the coherence terms of the density matrix goes to zero since β(t) is a random field.

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