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	Istituto Nazionale di Ottica, University of Florence
Citations	40
Analysis	Full AI Review Included

Executive Summary

This research experimentally verifies the quantum exchange fluctuation relation (FR) in an open quantum system using a solid-state platform.

Core Achievement: Successful experimental verification of the energy exchange fluctuation relation, G(ε) = 1, for a two-level system driven far from thermal equilibrium by non-unitary dynamics.
Platform: A single Nitrogen-Vacancy (NV) center spin qubit in diamond, operating at room temperature, utilized as a quantum simulator.
Mechanism: The open system dynamics are generated by repeated Quantum Projective Measurements (QPMs) induced by short laser pulses, combined with a tunable dissipation channel.
Key Finding (Energy Scale Factor): The fluctuation relation holds with a unique, time-independent energy scale factor, ε, which is determined solely by the difference in effective inverse temperatures (Δβ^(eff)) between the initial state and the asymptotic steady state (ε = Δβ^(eff)).
Protocol Robustness: The validity of the FR is shown to be robust, independent of the specific protocol parameters, including the Hamiltonian orientation, inter-pulse time intervals, and the stochastic nature of the QPM timing.
Theoretical Extension: Numerical simulations confirm that this result extends beyond two-level systems, holding true for a three-level system that reaches a steady state in the energy basis, suggesting broad applicability to generic finite-dimensional open systems.

Technical Specifications

The experiment utilizes a highly controlled solid-state qubit platform under ambient conditions.

Parameter	Value	Unit	Context
Qubit Platform	Single NV Center	N/A	Electronic spin S=1 in diamond lattice
Operating Temperature	Room Temperature	N/A	Ambient conditions
Qubit Levels	ms = 0 and ms = +1	N/A	Effective two-level system (ground state sublevels)
Magnetic Bias Field	394	G	Static field used for spin polarization
Microwave Detuning (δ) Range	0 to Ω	N/A	Used to tune the Hamiltonian (H)
Bare Rabi Frequency (Ω)	1.3	MHz	Frequency of the microwave driving field
Laser Wavelength	532	nm	Green laser used for QPM and spin pumping
Laser Pulse Duration (t_L)	41	ns	Duration of short laser pulses
Inter-Pulse Time (τ) Range	270 to 750	ns	Stochastic interval between QPMs
Spin-Conserving Emission Rate (Γ_eg)	77	MHz	Decay rate (from 7-level model fit)
Non-Radiative Decay Rate (Γ_1m)	60.4 ± 0.3	MHz	Decay rate to metastable singlet state
Effective Photon Absorption (P_abs)	18 to 68	%	Range of absorption probability used in protocols

Key Methodologies

The experiment employs a Two-Point Measurement (TPM) protocol on the NV center to characterize energy fluctuation statistics under controlled non-unitary dynamics.

Platform Setup: A single NV center in electronic-grade diamond is addressed using a home-built confocal microscope at ambient (room) temperature.
Qubit Control: The effective two-level system (ms=0, +1) is coherently manipulated using quasi-resonant continuous microwave (mw) driving, defining the time-independent Hamiltonian H.
Initial State Preparation (H-QPM): The system is initialized into a thermal state (or one of its energy eigenstates, |↑⟩ or |↓⟩) using optical pumping followed by a microwave rotation (R_y gate). This simulates the first energy measurement of the TPM protocol.
Non-Unitary Evolution: The system evolves under the Hamiltonian H interspersed with trains of short 532 nm laser pulses.
- QPM: Each laser pulse triggers a z-QPM (projection onto the σ_z basis), destroying coherence.
- Dissipation: The laser interaction also introduces a dissipation channel (non-radiative decay to the |0) state), driving the system toward an out-of-equilibrium steady state.
Final State Measurement (H-QPM): After the evolution time (t_fin), the final energy is measured using a final mw gate (R_y) followed by spin-selective fluorescence intensity readout.
Statistical Analysis: The conditional probabilities P_j|i are measured over a large ensemble of realizations to reconstruct the full statistics of the energy variation (ΔE) and calculate the characteristic function G(ε) = (exp(-εΔE)).

Commercial Applications

The fundamental research on quantum fluctuation relations and open quantum systems using NV centers has direct relevance to several emerging high-tech fields.

Quantum Thermodynamics:
- Design and optimization of nanoscale thermal devices, such as quantum heat engines and refrigerators, by understanding energy transport and efficiency limits imposed by fluctuation relations.
- Verification of generalized quantum fluctuation relations (QFRs) relevant to non-equilibrium processes.
Solid-State Quantum Computing and Simulation:
- NV centers serve as robust, room-temperature solid-state qubits, ideal for simulating complex open quantum system dynamics and testing fundamental physics principles.
- Developing methods to characterize and control dissipation and decoherence in solid-state quantum devices.
Quantum Sensing Technology:
- Exploiting the high degree of control over the NV spin degrees of freedom for advanced quantum sensing applications, including high-resolution magnetometry and thermometry, especially in ambient environments.
Advanced Diamond Materials:
- Consolidating the use of electronic-grade diamond as a platform for robust, high-performance quantum devices that can operate outside cryogenic environments.

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]