[Paper Review] Intrinsic and induced quantum quenches for enhancing qubit-based quantum noise spectroscopy

Yuxin Wang, Aashish A. Clerk|arXiv (Cornell University)|Apr 5, 2021

Quantum and electron transport phenomena79 references28 citations

TL;DR

This paper reveals that standard T2-based quantum sensing protocols inherently induce quantum quenches in the environmental bath due to sudden changes in the effective bath Hamiltonian at protocol onset. By analyzing the resulting quench phase shift (QPS), the authors demonstrate how this effect enables direct measurement of environmental temperature and reconstruction of spectral functions—offering a new, intrinsic sensing modality beyond standard decoherence measurements.

ABSTRACT

We discuss how standard $T_2$-based quantum sensing and noise spectroscopy protocols often give rise to an inadvertent quench of the system or environment being probed: there is an effective sudden change in the environmental Hamiltonian at the start of the sensing protocol. These quenches are extremely sensitive to the initial environmental state, and lead to observable changes in the sensor qubit evolution. We show how these new features can be used to directly access environmental response properties. This enables methods for direct measurement of bath temperature, and methods to diagnose non-thermal equilibrium states. We also discuss techniques that allow one to deliberately control and modulate this quench physics, which enables reconstruction of the bath spectral function. Extensions to non-Gaussian quantum baths are also discussed, as is the direct applicability of our ideas to standard diamond NV-center based quantum sensing platforms.

Motivation & Objective

• To identify and characterize unintended quantum quenches in standard T2-based quantum noise spectroscopy (QNS) protocols.
• To show that these quenches, arising from sudden changes in the effective bath Hamiltonian, are sensitive to the initial bath state and not just the coupling.
• To develop methods to use these quenches as a new sensing tool for measuring environmental temperature and spectral functions.
• To extend the framework to non-thermal and non-Gaussian bath states, enabling probing of nonequilibrium dynamics.
• To demonstrate the direct applicability of the quench-based sensing approach to existing platforms like NV centers in diamond.

Proposed method

• Formalize the effective bath Hamiltonian ˆHb,eff(t) as a time-dependent operator that undergoes a sudden change (quench) at t=0 due to the qubit's initial superposition state.
• Define the quench operator ˆV = ˆHb,eff(t=0+) − ˆHb,eff(t=0−) and the quench control function η(t) to model the temporal profile of the quench.
• Derive an analytical expression for the quench phase shift (QPS) as Φq(tf) = ∫ dt1 F(t1) ∫ dt2 η(t2) GRξV(t1−t2), linking it to the bath's dissipative susceptibility.
• Use the QPS in conjunction with standard decoherence measurements in a Hahn-echo protocol to extract environmental temperature for Ohmic baths.
• Demonstrate that the QPS is sensitive to initial bath states beyond thermal equilibrium, enabling diagnosis of nonequilibrium dynamics.
• Generalize the framework to non-Gaussian baths and show compatibility with standard NV-center sensing platforms.

Experimental results

Research questions

• RQ1 How do standard T2-based QNS protocols inadvertently induce quantum quenches in the environmental bath?
• RQ2 What is the physical origin and dependence of the quench phase shift (QPS) on the initial bath state?
• RQ3 Can the QPS be used to measure environmental temperature independently from decoherence data?
• RQ4 How can the QPS be leveraged to reconstruct the bath spectral function?
• RQ5 To what extent is this quench-based sensing framework applicable to non-thermal and non-Gaussian bath states?

Key findings

• The quench phase shift (QPS) is a direct consequence of an effective sudden change in the bath Hamiltonian at the start of a T2 protocol, even without intentional quenching.
• The QPS is not solely determined by the initial bath Hamiltonian but critically depends on the initial bath state, including non-thermal and nonequilibrium states.
• For an Ohmic bath, combining QPS measurements with standard decoherence data in a Hahn-echo protocol enables direct, independent extraction of the environmental temperature.
• The QPS provides a new probe of the bath's dissipative susceptibility, which is related to the effective density of states and can be used to reconstruct the spectral function.
• The framework generalizes beyond linear response and weak coupling, with applicability to non-Gaussian baths and realistic sensing platforms like NV centers.
• The QPS can be distinguished from external phase shifts and is sensitive to the initial qubit state, enabling new control and diagnostic capabilities in quantum sensing.