Experimental test of fluctuation relations for driven open quantum systems with an NV center
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-04-28 |
| Journal | New Journal of Physics |
| Authors | Santiago HernĂĄndez-GĂłmez, Nicolas Staudenmaier, Michele Campisi, Nicole Fabbri, Santiago HernĂĄndez-GĂłmez |
| Institutions | Istituto Nazionale di Ottica, University of Florence |
| Citations | 29 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis study presents the first experimental verification of quantum fluctuation relations (FRs) in driven open quantum systems, utilizing a single Nitrogen Vacancy (NV) center in diamond.
- Core Achievement: Successfully verified simplified forms of the general quantum fluctuation relation (Eq. 1) in a driven-dissipative environment where the system simultaneously exchanges work and heat.
- Platform: A single negatively-charged NV center spin qubit operating at room temperature, leveraging its long coherence time and precise optical/microwave (mw) addressability.
- Methodology: The system dynamics were engineered using continuous mw driving (work source) and intermittent short laser pulses (engineered dissipative channel/heat reservoir).
- Case 1 Verification: Confirmed the FR when the reservoir was set to an effective infinite pseudo-temperature (βR = 0), simplifying the relation to depend only on the system energy change (ÎE).
- Case 2 Verification: Confirmed the FR during cyclic driving at stroboscopic times where the total work performed on the system vanished (W=0), even though instantaneous power delivery was non-null.
- Significance: Establishes the NV center as a robust, room-temperature testbed for quantum thermodynamics, paving the way for future experiments requiring separate measurement of fluctuating work (W) and heat (Q).
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Quantum System | Single NV Center Spin Qubit | N/A | Ground state ms = 0, Âą1 manifold. |
| Operating Temperature | Room Temperature | K | Experimental environment. |
| External Magnetic Field (B) | 38.9 | mT | Aligned along the NV quantization axis to lift spin degeneracy. |
| Driving Field Type | Continuous Resonant Microwave (mw) | N/A | External work source (time-dependent Hamiltonian H(t)). |
| Bare Rabi Frequency (Ď0) | ~ (2Ď)800 | kHz | Used in the Hamiltonian H(t) for Section 4 experiments. |
| Dissipation Mechanism | Train of Short Laser Pulses | N/A | Engineered thermal reservoir (quantum map M). |
| Interpulse Spacing (Ď) | 410, 616, 1296, 308 | ns | Varied parameter for different driven-dissipative regimes. |
| Hamiltonian Period (TA) | 616 | ns | Period of the amplitude modulation Ď(t) in Section 3. |
| Initial Inverse Temperature (β) | 2/ħĎ0 | N/A | Effective temperature of the initial Gibbs state mixture used for statistical weighting. |
| Experimental Realizations | ~ 106 | Repetitions | Ensemble size for averaging conditional probabilities Pj|i(tf). |
| Asymptotic Probability (Pââ) | 0.050 to 0.509 | N/A | Determines the reservoir inverse pseudo-temperature (βR). |
Key Methodologies
Section titled âKey MethodologiesâThe experiment employed a three-step protocol (Initialization, Evolution, Readout) combined with engineered unitary and dissipative dynamics to emulate the two-point measurement scheme (TPMS) required for fluctuation relations.
-
Qubit Selection and Initialization:
- The two-level system is formed by the |ms = 0> and |ms = +1> states of the NV center ground spin.
- The spin is optically initialized into |0> using a long laser pulse.
- An opportune spin-rotating mw gate prepares the system into one of the initial Hamiltonian eigenstates (pÂą(0)).
-
Driven Evolution (Work Source):
- The system evolves under a time-dependent Hamiltonian H(t) provided by a continuous resonant mw driving field.
- Two types of driving were tested: time-varying amplitude (Section 3) and fixed amplitude with time-varying phase (Section 4).
-
Dissipative Channel Engineering (Heat Reservoir):
- The unitary evolution is intermittently perturbed by a train of temporally-equidistant short laser pulses (spacing Ď).
- Each pulse acts as a quantum projective measurement followed by Lindbladian dynamics, effectively opening a dissipative channel that drives the spin toward an asymptotic Gibbs state defined by the inverse pseudo-temperature βR.
-
Readout and Probability Construction:
- At the final time tf, the spin state is mapped back to the {|0>, |1>} basis and measured via photoluminescence intensity.
- The protocol is repeated to construct the conditional probabilities Pj|i(tf).
-
Fluctuation Relation Verification:
- The conditional probabilities are weighted by the initial Gibbs probability Pi(0) to emulate the TPMS on a thermal mixed state.
- Case 1 (Infinite T Reservoir): The Hamiltonian amplitude Ď(t) was varied periodically, and the laser pulses drove the system toward the completely mixed state (βR = 0). Verification involved checking <e-βÎE> = e-βÎF.
- Case 2 (Zero Work): A rotating Hamiltonian H(t) was used, and measurements were performed only at stroboscopic times tn = nĎθ, where the total work W vanished. Verification involved checking <e-(β-βR)ÎE> = 1.
Commercial Applications
Section titled âCommercial ApplicationsâThe technology and control methods demonstrated in this research are foundational for several high-value engineering and commercial applications, particularly those relying on high-quality diamond materials (relevant to CVD suppliers like 6ccvd.com).
| Application Area | Relevance to NV Center Technology | Material Requirements (CVD Context) |
|---|---|---|
| Quantum Sensing (Magnetometry/Thermometry) | NV centers are leading quantum sensors. This work demonstrates precise control over spin dynamics and engineered thermal contact, essential for optimizing sensor sensitivity and dynamic range in complex environments. | Requires ultra-high purity, low-strain single-crystal diamond (SC-CVD) to maximize coherence times (T2* and T2), ensuring stable qubit operation at room temperature. |
| Quantum Computing and Registers | NV centers serve as robust quantum register building blocks. The ability to engineer and control dissipation (heat exchange) is critical for efficient quantum state preparation, thermalization, and error correction protocols. | Precise control over nitrogen doping concentration during CVD growth is necessary to create isolated NV centers, followed by controlled irradiation/annealing processes. |
| Quantum Thermodynamics & Heat Engines | Provides a scalable, room-temperature platform for testing fundamental limits of energy conversion and entropy production in the quantum regime, informing the design of future nanoscale quantum devices. | Diamond substrates must maintain exceptional thermal stability and purity to ensure the NV center remains a well-isolated, controllable quantum system. |
| High-Power RF/Electronics | The diamond material itself, due to its high thermal conductivity, is crucial for heat management in high-power devices. The NV center control techniques developed here rely on the materialâs inherent stability. | CVD processes must deliver large-area, high-quality diamond wafers with controlled defect densities for integration into electronic and quantum devices. |
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 (HernĂĄndez-GĂłmez 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 timesâalthough 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.