Towards detecting traces of non-contact quantum friction in the corrections of the accumulated geometric phase

At a Glance

Metadata	Details
Publication Date	2020-02-19
Journal	npj Quantum Information
Authors	M. Belén Farías, Fernando C. Lombardo, Alejandro Soba, Paula I. Villar, Ricardo S. Decca
Institutions	University of Luxembourg, Fundación Ciencias Exactas y Naturales
Citations	35
Analysis	Full AI Review Included

Executive Summary

This research proposes a novel, experimentally viable method to detect traces of Quantum Friction (QF) indirectly by measuring corrections to the Geometric Phase (GP) of a moving quantum system.

Core Value Proposition: The study establishes a robust scenario for tracking QF traces by observing the velocity dependence of decoherence effects on a solid-state qubit (NV center in diamond).
Quantum Friction Detection: QF, a contactless dissipative force, is tracked by measuring the correction (δφ) to the unitary Geometric Phase (GP) as the particle moves relative to a dielectric sheet.
Feasibility: The system maintains high quantum purity (low decoherence) for several tens of cycles, allowing the GP to accumulate sufficiently for measurement before phase information is lost.
Key Measurement Target: The velocity-induced correction (δφ_u≠0) becomes relevant at relatively short timescales, distinguishing it from corrections induced solely by the static presence of the dielectric sheet (δφ_u=0).
Experimental Setup: The proposed scheme utilizes a single Nitrogen-Vacancy (NV) center in a diamond tip mounted on a modified Atomic Force Microscope (AFM) cantilever, moving over a rotating, metal-coated Silicon disk.
Measurability: State-of-the-art phase detection technology (50 mrad over 10⁶ repetitions) is sufficient to measure the predicted velocity-dependent phase shift, particularly when using n-doped Si coating.

Technical Specifications

Parameter	Value	Unit	Context
NV Center Gap Distance (a)	3 to 10	nm	Separation between AFM tip (NV center) and Si disk.
Gap Control Resolution (δa)	1	nm	Required uniformity maintained by AFM feedback control.
Turntable Angular Velocity (Ω)	2π * 7000	rad/s	Maximum rotation speed of the 12 cm diameter Si disk.
Turntable Wobble	10^-8	radians	Vertical motion at the edge of the disk (equivalent to 1 nm).
Measurable Phase Change	50	mrad	Detection limit over 10⁶ repetitions using state-of-the-art NV center phase detection.
Au Plasma Frequency (ω_pl)	1.37 x 10¹⁶	rad/s	Drude-Lorentz model parameter for Gold coating.
Au Dissipation Ratio (Γ/ω_pl)	~0.05	Dimensionless	Weak dissipation limit for Gold coating.
n-Si Plasma Frequency (ω_pl)	3.5 x 10¹⁴	rad/s	Drude-Lorentz model parameter for n-doped Silicon.
n-Si Dissipation Ratio (Γ/ω_pl)	~1	Dimensionless	Dissipation limit for n-doped Silicon.
Dimensionless Velocity (u)	0.0025	Dimensionless	Achievable velocity parameter for n-doped Si coating (u = v/(aω_pl)).
System Purity Retention	~30	Cycles (N)	Number of cycles the state vector maintains high purity (R(t) near 1).

Key Methodologies

The proposed experiment relies on combining high-precision nanomechanical control (AFM) with quantum sensing (NV center) to measure the accumulated Geometric Phase (GP) correction.

System Modeling: The neutral particle (atom/NV center) is modeled as a two-level system (energy level spacing Δ) coupled via dipolar interaction to the quantum vacuum field, which is dressed by the presence of the dielectric sheet.
Non-Unitary Evolution Calculation: The dynamics are governed by a master equation incorporating velocity-dependent diffusion coefficients D(v, t) and f(v, t), and dissipative effects ζ(v, t). These coefficients are derived from noise and dissipation kernels v(t) and n(t).
Geometric Phase (GP) Computation: The GP (φ_g) is calculated using the kinematic approach for open systems, derived from the eigenvalues and eigenvectors of the reduced density matrix ρ(t) obtained by solving the master equation.
Experimental Setup (AFM/NV Center):
- A single NV center in a diamond tip is mounted on an AFM cantilever, serving as the two-level quantum system.
- The sample is a 12 cm diameter Si disk coated with metal (Au or n-doped Si) mounted on a high-speed turntable (up to 7000 Hz).
Gap Control: The AFM system maintains a constant, nanometer-scale gap (a = 3-10 nm) between the NV center and the rotating disk, controlling the separation within 1 nm (δa).
Velocity Dependence Measurement: The correction to the GP (δφ = φ_g - φ_c) is measured as a function of the tangential velocity (v) of the NV center relative to the disk. The velocity contribution (δφ_u≠0) is isolated by subtracting the static correction (δφ_u=0).
Phase Detection: High-fidelity phase detection techniques are employed to measure the accumulated phase shift over millions of cycles, aiming for the detection limit of 50 mrad over 10⁶ repetitions.

Commercial Applications

The ability to precisely measure and understand non-contact quantum friction and related decoherence effects has direct implications for advanced micro- and nanomechanical systems and quantum technologies.

Quantum Sensing and Metrology:
- Development of high-precision thermometers based on GP encoding of thermal states.
- Creation of highly sensitive sensors for measuring environmental noise and dissipation kernels in quantum systems.
Nanomechanical Systems (NEMS/MEMS):
- Improved design and operation of micro- and nanomechanical devices (e.g., resonators, actuators) where non-contact friction is a critical limiting factor.
- Better understanding of energy dissipation mechanisms in nanoscale moving parts.
Quantum Computing and Information:
- Optimization of solid-state qubits (like NV centers) by characterizing and mitigating environmentally induced decoherence and dissipation during dynamic operations.
- Development of robust geometric phase gates, which are topologically protected against certain noise sources.
Advanced Materials Characterization:
- Non-contact characterization of the electromagnetic properties (plasma frequency, dissipation) of novel materials like graphene or topological insulators under dynamic conditions.

View Original Abstract

Abstract The geometric phase can be used as a fruitful venue of investigation to infer features of the quantum systems. Its application can reach new theoretical frontiers and imply innovative and challenging experimental proposals. Herein, we take advantage of the geometric phase to sense the corrections induced while a neutral particle travels at constant velocity in front of an imperfect sheet in quantum vacuum. As it is already known, two bodies in relative motion at constant velocity experience a quantum contactless dissipative force, known as quantum friction. This force has eluded experimental detection so far due to its small magnitude and short range. However, we give details of an innovative experiment designed to track traces of the quantum friction by measuring the velocity dependence of corrections to the geometric phase. We notice that the environmentally induced corrections can be decomposed in different contributions: corrections induced by the presence of the dielectric sheet and the motion of the particle in quantum vacuum. As the geometric phase accumulates over time, its correction becomes relevant at a relative short timescale, while the system still preserves purity. The experimentally viable scheme presented would be the first one in tracking traces of quantum friction through the study of decoherence effects on a NV center in diamond.

Tech Support

Original Source

DOI: https://doi.org/10.1038/s41534-020-0252-x

References

2003 - The Quantum Vacuum
2009 - Advances in the Casimir Effect [Crossref]
2001 - The Casimir Effect: Physical Manifestations of the Zero- Point Energy [Crossref]