Cyclic cooling of quantum systems at the saturation limit

At a Glance

Metadata	Details
Publication Date	2021-06-03
Journal	npj Quantum Information
Authors	Sebastian Zaiser, Chun Tung Cheung, Sen Yang, Durga Bhaktavatsala Rao Dasari, Sadegh Raeisi
Institutions	University of Stuttgart, Sharif University of Technology
Citations	14
Analysis	Full AI Review Included

Executive Summary

Core Achievement: Experimental demonstration of Heat-Bath Algorithmic Cooling (HBAC) using a single Nitrogen-Vacancy (NV) center in diamond to hyperpolarize a target ¹⁴N nuclear spin.
Performance Limit: The experiment successfully reached the theoretical asymptotic cooling limit predicted for HBAC, significantly surpassing the polarization achievable via standard Dynamic Nuclear Polarization (DNP).
System Architecture: The NV electron spin acts as a dual-purpose quantum machine: it serves as the active heat-bath for resetting the two ¹³C nuclear spins and mediates the quantum gates (Toffoli/SWAP) required for entropy compression.
Engineering Implementation: The cyclic cooling algorithm was implemented using high-fidelity, spectrally selective quantum gates optimized via the DYNAMO optimal control package.
Fidelity Metrics: High operational fidelity was maintained, including a nuclear spin initialization fidelity of ~99% (for reset spins) and a ¹⁴N readout fidelity of ~97%.
Significance: This method provides a robust pathway for achieving near-unit polarization in target nuclear spins, critical for enhancing the Signal-to-Noise Ratio (SNR) in nanoscale NMR sensing applications.

Technical Specifications

Parameter	Value	Unit	Context
Diamond Material	Type IIa CVD	N/A	Substrate for NV center
¹³C Concentration	0.2	%	Background isotope concentration
NV Center Depth	~15	µm	Below diamond surface
Static Magnetic Field (B₀)	~540	mT	Aligned along NV symmetry (z) axis
Optical Excitation Wavelength	532	nm	Used for electron spin polarization
Electron-¹⁴N Coupling (A_zz)	-2.16	MHz	Hyperfine coupling strength
Electron-¹³C₂ Coupling (A_zz)	414	kHz	Strongest ¹³C hyperfine coupling
Electron-Controlled Nuclear Gate Time	50	µs	Typical duration for nuclear spin gates
Nuclear-Controlled Electron Gate Time	~28	µs	Typical duration for electron spin gates
Single Toffoli Gate Duration	~285	µs	Implements the core HBAC transformation
Total Iteration Time	~6	ms	Time per full HBAC cycle (including reset)
Nuclear Spin Readout Fidelity	~97	%	Single-shot readout method
Reset Spin Initialization Fidelity	~99	%	Achieved via 25 repetitions of SWAP gate

Key Methodologies

The experimental implementation of HBAC relies on precise control of the NV center in a diamond host:

Sample and Setup:
- Used a Type IIa CVD diamond crystal (0.2% ¹³C) with the NV center located ~15 µm deep.
- A coplanar waveguide was fabricated on the diamond surface for Microwave (MW) and RF excitation.
- Experiments were conducted using a home-built confocal microscope at room temperature.
Magnetic Field Application:
- A permanent magnet provided a static field (B₀ ~540 mT) aligned along the NV center’s symmetry axis (z-axis) to define the quantization axis and lift spin degeneracies.
Electron Spin Initialization (Heat-Bath Function):
- A 532 nm laser optically pumps the NV electron spin into the m_s=0 state, establishing it as the polarized heat-bath and the source of polarization.
Nuclear Spin Reset (¹³C Reset Qubits):
- The ¹³C reset spins are initialized by transferring polarization from the electron spin via repetitive SWAP gates. This process is non-unitary and achieves variable polarization levels, crucial for exploring the HBAC polarization space.
Algorithmic Cooling Cycle:
- The core HBAC operation (U_e, a three-qubit gate) is implemented, which effectively swaps the population between the target ¹⁴N spin and the two ¹³C reset spins.
- The quantum gates required for U_e are mediated by the strongly coupled electron spin, enabling fast and high-fidelity control over the nuclear spins.
Gate Optimization and Control:
- All quantum gates were optimized using the DYNAMO optimal control package to ensure spectral selectivity and minimize errors arising from cross-talk in the dense electron hyperfine spectrum.
Polarization Measurement:
- The final polarization of the target ¹⁴N spin was measured using a high-fidelity single-shot readout method. The cycle was repeated 25 times to observe convergence to the theoretical HBAC limit.

Commercial Applications

The ability to achieve extreme hyperpolarization in nuclear spins using NV centers has direct implications for several high-tech sectors:

Quantum Sensing and Metrology:
- Nanoscale NMR: HBAC provides the necessary high initial polarization to dramatically boost the SNR for NMR experiments on picoliter volumes, enabling chemical analysis with nanoscale resolution (e.g., analyzing molecules external to the diamond surface).
- Precision Magnetometry: Highly polarized nuclear spins can serve as ultra-sensitive probes for detecting weak magnetic fields or measuring chemical shifts with enhanced sensitivity.
Quantum Information Processing:
- Quantum Memory and Initialization: The technique offers a robust method for initializing nuclear spin qubits (which possess long coherence times, T₁ ~1 s for ¹³C) to a near-pure state, a prerequisite for scalable quantum computation.
Biomedical Imaging:
- Hyperpolarized MRI Agents: The principles of hyperpolarization are foundational to creating highly sensitive contrast agents for Magnetic Resonance Imaging (MRI), potentially enabling real-time metabolic imaging in clinical settings.
Quantum Thermodynamics:
- Quantum Heat Engines: The experimental setup serves as a demonstration platform for studying the fundamental limits and efficiency of microscopic quantum heat engines and refrigerators based on cyclic algorithmic cooling.

Tech Support

Original Source

DOI: https://doi.org/10.1038/s41534-021-00408-z