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Experimental test of fluctuation relations for driven open quantum systems with an NV center

MetadataDetails
Publication Date2021-04-28
JournalNew Journal of Physics
AuthorsSantiago HernĂĄndez-GĂłmez, Nicolas Staudenmaier, Michele Campisi, Nicole Fabbri, Santiago HernĂĄndez-GĂłmez
InstitutionsIstituto Nanoscienze, University of Florence
Citations29
AnalysisFull AI Review Included

Technical Analysis: Quantum Fluctuation Relations in Driven Open Systems using NV Centers

Section titled “Technical Analysis: Quantum Fluctuation Relations in Driven Open Systems using NV Centers”

This document analyzes the research paper “Experimental test of fluctuation relations for driven open quantum systems with an NV center” and outlines how 6CCVD’s specialized MPCVD diamond materials and engineering capabilities directly support and enable this advanced quantum thermodynamics research.


The research successfully verifies quantum fluctuation relations (FRs) in a driven-dissipative open quantum system using a single Nitrogen-Vacancy (NV) center in diamond. This work represents a significant milestone in experimental quantum thermodynamics.

  • Platform Validation: The study confirms the NV center in Single Crystal Diamond (SCD) as a robust, optically addressable platform for exploring non-equilibrium thermodynamics in the quantum regime.
  • Core Achievement: Experimental verification of simplified quantum fluctuation relations (Eq. 6 and Eq. 7) in two complex scenarios: infinite pseudo-temperature reservoir ($\beta_R = 0$) and zero total work at stroboscopic times.
  • Methodology: The experiment relies on precise coherent control (continuous microwave driving) and engineered dissipation (intermittent short laser pulses) applied to the NV electronic spin ground state.
  • Key Parameters: Experiments required high statistical fidelity, achieved through $\sim 10^6$ repetitions, and precise timing control (pulse spacing $\tau$ in the hundreds of nanoseconds range).
  • Material Requirement: The success of this experiment is fundamentally dependent on the long coherence times and stability provided by high-quality, low-strain SCD substrates.
  • Future Impact: The results pave the way for a full experimental demonstration of the general fluctuation relation (Eq. 1) involving simultaneous heat and work exchange.

The following hard data points were extracted from the experimental setup and results:

ParameterValueUnitContext
Qubit PlatformSingle NV CenterN/AElectronic spin ground state in diamond.
Operating TemperatureRoom Temperature°CEnvironment for the NV center.
External Magnetic Field (B)38.9mTAligned along the NV quantization axis to lift degeneracy.
Initial Inverse Temperature ($\beta$)$2 / \hbar \omega_0$N/AUsed to weight initial states for Gibbs probability $P_{\pm}(0)$.
Laser Pulse Spacing ($\tau$)410, 616nsTime between consecutive short laser pulses (dissipative map).
Hamiltonian Period ($\tau_A$)616nsUsed for synchronization in infinite T reservoir case.
Floquet Period ($\tau_\theta$)308, 616, 1296nsUsed for work vanishing at stroboscopic times.
Bare Rabi Frequency ($\omega_0$)$\sim (2\pi)800$kHzFixed amplitude of the microwave driving field.
Experimental Repetitions$\sim 10^6$N/ARequired ensemble size for statistical averaging of conditional probabilities.
Reservoir Inverse Pseudo-Temperature ($\beta_R$)0N/AMimics an effective infinite-temperature reservoir (Sec. 3).

The experimental protocol utilized a combination of optical, magnetic, and microwave control techniques on the NV center:

  1. Qubit Definition: The electronic spin ground state of the NV center was used to form a two-level system basis, $|m_s = 0\rangle$ and $|m_s = \pm 1\rangle$, with degeneracy removed by a $38.9 \text{ mT}$ magnetic field.
  2. Initialization: The system was optically initialized into $|0\rangle$ using a long laser pulse, followed by a spin-rotating microwave gate to prepare the system in a specific initial Hamiltonian eigenstate ($\rho_{\pm}(0)$).
  3. Driven Evolution: The system evolved under a time-dependent Hamiltonian $H(t)$ generated by a continuous resonant microwave (mw) driving field, providing the external work source.
  4. Dissipative Channel: A train of temporally-equidistant short laser pulses was applied intermittently. Each pulse acts as a quantum projective measurement, opening a dissipative channel that mimics interaction with a thermal reservoir $R$.
  5. Readout: At the final time $t_f$, the spin state was measured by mapping it back to the ${|0\rangle, |1\rangle}$ basis and recording the NV photoluminescence intensity.
  6. Statistical Reconstruction: Conditional probabilities $P_{j|i}(t_f)$ were measured over $\sim 10^6$ repetitions and combined with the initial Gibbs probability $P_i(0)$ to reconstruct the energy change probability distribution $p(\Delta E)$.

The successful execution of this quantum thermodynamics research hinges on the quality and customization of the diamond substrate. 6CCVD provides the necessary high-specification MPCVD diamond materials and engineering services required to replicate, scale, and advance this work.

Research Requirement6CCVD Solution & CapabilityTechnical Advantage
High-Coherence NV PlatformOptical Grade Single Crystal Diamond (SCD)Our SCD is grown via MPCVD with ultra-low nitrogen content, ensuring minimal paramagnetic impurities and maximizing NV center coherence time ($T_2$), which is critical for high-fidelity quantum control and long experimental protocols.
Precise Surface QualitySCD Polishing: $R_a < 1 \text{ nm}$.Minimizes surface roughness and strain, reducing decoherence mechanisms and improving the stability of near-surface NV centers essential for robust quantum measurements.
Custom Substrate DimensionsCustom Plates/Wafers up to $125 \text{ mm}$ (PCD) and custom SCD sizes.Provides the necessary flexibility for integrating diamond into complex experimental setups, including custom optical access or large-scale quantum device integration.
On-Chip Microwave IntegrationCustom Metalization Services (Au, Pt, Ti, Cu, W).We offer in-house deposition of thin-film metals for creating high-performance microwave striplines or antennas directly on the diamond surface, enabling precise control over the Rabi frequency $\omega(t)$ and the time-dependent driving field $H(t)$.
Thickness OptimizationSCD thickness control from $0.1 \text{ ”m}$ to $500 \text{ ”m}$.Allows researchers to specify optimal thickness for thermal management, strain reduction, and integration with specific optical microscopy or cryo-systems.
Engineering Support for Quantum ProjectsIn-house PhD team specializing in MPCVD growth and quantum material selection.Our experts can consult on optimizing diamond specifications (e.g., controlled nitrogen doping for NV creation, surface termination) to meet the exact requirements for advanced quantum sensing and thermodynamics experiments.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. We offer global shipping (DDU default, DDP available) to ensure your research materials arrive quickly and reliably.

View Original Abstract

Abstract The experimental verification of quantum fluctuation relations for driven open quantum system is currently a challenge, due to the conceptual and operative difficulty of distinguishing work and heat. The nitrogen-vacancy (NV) center in diamond has been recently proposed as a controlled test bed to study fluctuation relations in the presence of an engineered dissipative channel, in absence of work (Hernández-Gómez et al 2020 Phys. Rev. Res. 2 023327). Here, we extend those studies to exploring the validity of quantum fluctuation relations in a driven-dissipative scenario, where the spin exchanges energy both with its surroundings because of a thermal gradient, and with an external work source. We experimentally prove the validity of the quantum fluctuation relations in the presence of cyclic driving in two cases, when the spin exchanges energy with an effective infinite-temperature reservoir, and when the total work vanishes at stroboscopic times—although the power delivered to the NV center is non-null. Our results represent the first experimental study of quantum fluctuation relation in driven open quantum systems.