Experimental test of exchange fluctuation relations in an open quantum system

At a Glance

Metadata	Details
Publication Date	2020-06-12
Journal	Physical Review Research
Authors	S. Hernández Gómez, S. Gherardini, F. Poggiali, F. S. Cataliotti, A Trombettoni
Institutions	Massachusetts Institute of Technology, Istituto Nazionale di Ottica
Citations	40
Analysis	Full AI Review Included

6CCVD Technical Documentation: Quantum Fluctuation Relations in Open NV-Diamond Systems

Executive Summary

This research utilizes the robust properties of the Nitrogen-Vacancy (NV) center in diamond to experimentally verify the Energy Exchange Fluctuation Relation in an out-of-equilibrium open quantum system. The findings validate key theoretical concepts essential for designing future quantum heat engines and simulators.

Core Achievement: Verification of the energy exchange fluctuation relation, $G(\epsilon) = 1$, for a single NV center spin qubit operating as an open two-level quantum system.
Platform Validation: Establishes the NV center in electronic-grade diamond as a highly controllable quantum simulator for studying non-equilibrium thermodynamics and dissipative quantum dynamics.
Key Finding: Confirmed the existence of a unique, time-independent energy scale factor $\epsilon$ that successfully encodes missing reservoir information within the system’s out-of-equilibrium steady state properties.
Methodology: Employed a Two-Point Measurement (TPM) protocol combining microwave-driven unitary evolution with non-unitary dynamics induced by repeated short 532 nm laser pulses (Quantum Projective Measurements and controlled dissipation).
Material Requirement: Requires exceptionally high-purity Single Crystal Diamond (SCD) with ultra-low nitrogen concentration (< 5 ppb) to ensure the long coherence times and minimal environmental noise necessary for stable qubit operation at ambient conditions.
6CCVD Advantage: 6CCVD provides the necessary electronic-grade MPCVD SCD substrates and customized metalization to replicate and scale this foundational quantum research.

Technical Specifications

The following parameters define the experimental platform and observed dynamic rates crucial for replicating or advancing this research.

Parameter	Value	Unit	Context
Diamond Material Purity	< 5	ppb N	Required concentration for electronic grade SCD (14-N)
System Qubit	Single NV Center	N/A	Focused on $m_s = 0$ and $m_s = +1$ sublevels (Effective two-level system)
Static Magnetic Bias Field	394	G	Used for spin polarization and degeneracy removal
Excitation Wavelength	532	nm	Green laser light used for Quantum Projective Measurements (QPMs)
Short Laser Pulse Duration ($t_L$)	41	ns	Duration of single laser pulses
Inter-Pulse Time ($\tau$) Range	270 < $\tau$ < 750	ns	Stochastic distribution interval for QPMs
Bare Rabi Frequency ($\Omega$)	1.3	MHz	Coherent manipulation frequency set by microwave driving
Spontaneous Emission Rate ($\Gamma_{eg}$)	77	MHz	Spin-preserving radiative transition rate
Metastable Decay Rate ($\Gamma_{1m}$)	60.4 ± 0.3	MHz	Non-radiative decay rate affecting dissipation channel

Key Methodologies

The experiment employed a specialized Two-Point Measurement (TPM) protocol on the NV center qubit to characterize the statistics of energy fluctuations under non-unitary dynamics.

Platform Initialization: A single NV center in high-purity SCD was optically spin-pumped into the $|0\rangle$ state, and a strong static magnetic field (394 G) was applied to remove spin degeneracy and polarize the nuclear spin.
Initial Energy Measurement (H-QPM): The system was prepared in one of its thermal energy eigenstates (|↑⟩ or |↓⟩) using optical pumping and specific microwave (mw) gates ($R_y$) to establish the initial density matrix $\rho_{in}$.
Evolution and Dissipation: The system underwent unitary evolution set by the microwave Hamiltonian ($H$) interspersed with non-unitary dynamics. This non-unitary component consisted of trains of short 532 nm laser pulses (41 ns duration) that implemented $\sigma_z$ Quantum Projective Measurements (z-QPMs) combined with controlled spin amplitude damping (dissipation channel).
Steady State Dynamics: The combined QPM and dissipation effects drove the system toward an asymptotic out-of-equilibrium steady state, characterized by energy fluctuations and coherence modification.
Final Energy Measurement (H-QPM): At time $t_{fin}$, a final energy measurement was performed. A mw gate ($R_y^{\alpha}$) mapped the Hamiltonian basis states onto the $\sigma_z$ basis, followed by a spin-selective fluorescence readout, repeated $\sim 1.6 \times 10^6$ times to reduce photon shot noise and measure conditional probabilities ($P_{j|i}$).
Flutuation Verification: The resulting conditional probabilities were used to calculate the mean exponentiated energy fluctuation $\langle \exp(-\epsilon \Delta E) \rangle$, verifying the relation equals 1, where $\epsilon = \Delta\beta^{(eff)}$ relates the effective inverse temperatures of the initial and final states.

6CCVD Solutions & Capabilities

Replicating and scaling this critical research in quantum thermodynamics depends fundamentally on access to highly specialized diamond materials. 6CCVD is an expert technical partner capable of providing all necessary material specifications and engineering customization.

Applicable Materials

The foundation of this experiment—the stable, controllable NV center—requires diamond with the lowest possible paramagnetic defects to maintain spin coherence ($T_2$).

Application Requirement	6CCVD Solution	Material Specification
High Spin Coherence	Electronic Grade Single Crystal Diamond (SCD)	Nitrogen Concentration: < 5 ppb (Ultra-low)
Optical Access/Low Absorption	Optical Grade MPCVD Diamond	CVD Growth with superior lattice quality (Essential for 532 nm laser integration)
Substrate Dimensions	Custom SCD Plates/Wafers	Up to 125 mm diameter; Substrates up to 10 mm thickness

Customization Potential

The experimental setup suggests the need for precise substrate preparation and potential integration of control electronics.

Precision Polishing: Qubit performance, especially when shallow NV centers are desired, relies on pristine surface quality. 6CCVD provides epitaxial-ready polishing for SCD, achieving surface roughness of Ra < 1 nm, which is necessary for stable near-surface NV operation.
Custom Dimensions and Orientation: 6CCVD offers custom laser cutting and shaping of diamond plates to fit specialized cryostats or high-field setups. We also supply specific crystal orientations (e.g., [111] vs [100]) crucial for optimized NV axis alignment.
Integrated Metalization: To transition from tabletop experiments (using external microwave coils) to scalable quantum chips, integrated control lines are necessary. 6CCVD provides internal fabrication of custom metalization stacks (e.g., Ti/Pt/Au or Cu/W) directly patterned onto the diamond surface for integrated microwave routing and signal delivery.

Engineering Support

Understanding the material science required to host a functional quantum system is our specialty.

Process Expertise: 6CCVD’s in-house PhD team provides consultative support on material selection, NV creation methodology (e.g., controlled ion implantation depths), and annealing recipes to ensure the final substrate meets the specific demands of Open Quantum System Thermodynamics projects.
Thermal Management: The research hints at quantum heat engines. 6CCVD can assist in designing diamond components that leverage the material’s exceptional thermal properties for high-efficiency quantum engine or refrigeration applications.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Elucidating the energy transfer between a quantum system and a reservoir is a central issue in quantum non-equilibrium thermodynamics, which could provide novel tools to engineer quantum-enhanced heat engines. The lack of information on the reservoir inherently limits the practical insight that can be gained on the exchange process of open quantum systems. Here, we investigate the energy transfer for an open quantum system in the framework of quantum fluctuation relations. As a novel toolbox, we employ a nitrogen-vacancy center spin qubit in diamond, subject to repeated quantum projective measurements and a tunable dissipation channel. In the presence of energy fluctuations originated by dissipation and quantum projective measurements, the experimental results, supplemented by numerical simulations, show the validity of the energy exchange fluctuation relation, where the energy scale factor encodes missing reservoir information in the system out-of-equilibrium steady state properties. This result is complemented by a theoretical argument showing that, also for an open three-level quantum system, the existence of an out-of-equilibrium steady state dictates a unique time-independent value of the energy scale factor for which the fluctuation relation is verified. Our findings pave the way to the investigation of energy exchange mechanisms in arbitrary open quantum systems.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevresearch.2.023327

References

2017 - Nonequilibrium Statistical Physics: A Modern Perspective [Crossref]