Thermodynamics of a Minimal Algorithmic Cooling Refrigerator

At a Glance

Metadata	Details
Publication Date	2022-07-11
Journal	Physical Review Letters
Authors	Rodolfo R. Soldati, Durga Dasari, Jörg Wrachtrup, Eric Lutz
Institutions	University of Stuttgart, Max Planck Institute for Solid State Research
Citations	11
Analysis	Full AI Review Included

6CCVD Technical Documentation: MPCVD Diamond for Quantum Thermodynamics

Executive Summary

This research validates the use of high-purity MPCVD diamond hosting Nitrogen-Vacancy (NV) centers as a robust platform for studying quantum thermodynamics and building minimal quantum thermal machines.

Core Achievement: Experimental demonstration and analytical modeling of a minimal three-qubit heat-bath algorithmic cooling refrigerator using the electron and nuclear spins of an NV center in diamond.
Material Validation: Confirms that high-coherence, low-strain diamond is essential, enabling nuclear spin lifetimes ($T_1$) on the order of seconds and electron spin coherence times ($T_{2e}^{Hahn}$) up to $\sim 395$ µs.
Thermodynamic Performance: Successfully measured the Coefficient of Performance (COP) and cooling power $J(n)$, showing values close to the fundamental Carnot bounds in the reversible limit ($\gamma \rightarrow 0$).
Realistic Modeling: The theoretical framework explicitly accounts for experimentally relevant imperfections, including external damping ($\gamma \sim 10^{-4}$) and nonideal gate implementation (mixing angle $\theta \sim \pi/3.4$).
6CCVD Value Proposition: 6CCVD specializes in providing the high-quality Single Crystal Diamond (SCD) substrates necessary to replicate and advance this research, offering custom dimensions and integrated metalization for complex quantum control circuitry.

Technical Specifications

The following hard data points were extracted from the experimental validation of the three-qubit algorithmic cooling refrigerator:

Parameter	Value	Unit	Context
Qubit System	3-Qubit	N/A	NV Center in Diamond ($^{14}$N target, two $^{13}$C resets)
Magnetic Field Strength	540	mT	Applied via permanent magnet for high-fidelity readout
Target Spin Larmor Frequency ($^{14}$N)	$\sim 1.66$	MHz	Frequency of the target qubit
Nuclear Spin Lifetime ($T_1$)	Seconds	N/A	Allows multiple cooling cycles
Electron Spin Coherence ($T_{2e}^{Hahn}$)	$\sim 395$	µs	Coherence time of the central electron spin
Target Qubit Decay Rate ($\gamma$)	$\sim 10^{-4}$	N/A	Experimentally relevant damping rate
Optimal Mixing Angle ($\theta$)	$\pi/3.4$	Radians	Corresponds to $\sim 20%$ compression error
Total Gate Duration ($U$)	$\sim 284$	µs	Duration of the compression operation
Compression Step Time	$\sim 285$	µs	Time for the compression gate
Refresh Step Time	$\sim 5$	ms	Time for the reset spins to rethermalize
Extracted Heat ($Q(n)$) per cycle	Few	neV	Order of magnitude
Cooling Power ($J(n)$)	Few	µeV/s	Order of magnitude (or $10^{-26}$ W)

Key Methodologies

The experiment utilized a three-qubit spin register within a single NV center in diamond, controlled via optical, microwave (MW), and radio frequency (RF) techniques.

Substrate and Sample:
- Diamond sample embedded in a 2 mm thick, 50 mm diameter sapphire wafer.
- Experiment conducted at ambient conditions (room temperature, atmospheric pressure).
Optical Control and Initialization:
- 520 nm laser (0.1 mW to 0.5 mW) used for NV center saturation and electron spin polarization.
- 637 nm laser (< 10 µW) used for electron spin repolarization (charge state control).
- Electron spin initialized to the $|m_s = 0\rangle$ state.
Spin Manipulation and Gates:
- MW and RF sources used for high-fidelity control of electron and nuclear spins.
- Compression Step: Implemented via a non-local three-qubit Toffoli gate mediated by the electron spin.
- Refresh Step: Implemented via a simplified SWAP gate (two CNOT gates) to transfer electron spin polarization to the $^{13}$C reset spins.
Thermodynamic Measurement:
- Qubit polarizations $\epsilon_i(n)$ were measured using single-shot readout (SSR).
- Heat $Q(n)$ and Work $W(n)$ were derived analytically from the measured target qubit polarization $\epsilon_1(n)$.

6CCVD Solutions & Capabilities

6CCVD is uniquely positioned to supply the foundational diamond materials and custom engineering required to replicate and scale this quantum thermodynamic research.

Applicable Materials for Quantum Refrigeration

The success of this experiment hinges on the long coherence times and low defect density provided by high-quality SCD.

6CCVD Material Recommendation	Specification & Relevance
Optical Grade SCD (Type IIa)	Ultra-low nitrogen content (< 1 ppb) ensures minimal background spin noise and maximizes $T_{2e}^{Hahn}$ and nuclear $T_1$ times, critical for high-fidelity quantum gates.
Custom SCD Substrates	SCD plates available in thicknesses from 0.1 µm up to 500 µm, allowing optimization for specific NV implantation depths and thermal management.
High Purity PCD	For applications requiring larger area coverage (up to 125 mm diameter) where the NV center is not required, 6CCVD offers high-purity PCD with Ra < 5 nm polishing.

Customization Potential & Engineering Services

The experimental setup utilized a specific diamond/sapphire integration and complex RF control. 6CCVD offers tailored solutions to meet these advanced engineering requirements:

Custom Dimensions and Substrates: The paper used a 50 mm diameter wafer. 6CCVD can supply custom SCD plates up to 10 mm thick and PCD wafers up to 125 mm diameter, matching or exceeding the required dimensions for scaling up quantum devices.
Advanced Polishing: To ensure optimal optical access for the 520 nm and 637 nm lasers, 6CCVD guarantees ultra-smooth surfaces: Ra < 1 nm for SCD and Ra < 5 nm for inch-size PCD.
Integrated Metalization: Quantum control requires precise MW/RF delivery. 6CCVD offers in-house metalization services (Au, Pt, Pd, Ti, W, Cu) for patterning on-chip microwave transmission lines (e.g., coplanar waveguides) directly onto the diamond surface, simplifying experimental integration.
Substrate Integration: We offer consultation and manufacturing support for mounting and integrating diamond films onto secondary substrates, such as the sapphire wafer used in this study, ensuring mechanical stability and thermal performance.

Engineering Support

6CCVD’s in-house PhD team specializes in material science for quantum applications. We can assist researchers in selecting the optimal diamond specifications (e.g., nitrogen concentration, crystal orientation, and surface termination) required to replicate or extend this quantum algorithmic cooling research, particularly concerning the trade-offs between damping rate ($\gamma$) and gate fidelity ($\theta$).

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

View Original Abstract

We investigate, theoretically and experimentally, the thermodynamic performance of a minimal three-qubit heat-bath algorithmic cooling refrigerator. We analytically compute the coefficient of performance, the cooling power, and the polarization of the target qubit for an arbitrary number of cycles, taking realistic experimental imperfections into account. We determine their fundamental upper bounds in the ideal reversible limit and show that these values may be experimentally approached using a system of three qubits in a nitrogen-vacancy center in diamond.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevlett.129.030601

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