Intrinsic and induced quantum quenches for enhancing qubit-based quantumn noise spectroscopy
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2021-04-05 |
| Journal | arXiv (Cornell University) |
| Authors | Yuxin Wang, Aashish A. Clerk |
| Institutions | University of Chicago |
| Citations | 28 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”- Enhanced Quantum Noise Spectroscopy (QNS): The research introduces a method to enhance standard T2-based QNS protocols by leveraging the physics of quantum quenches—sudden changes in the effective environmental Hamiltonian at the start of the sensing protocol.
- Quench Phase Shift (QPS) as a New Probe: This quench generates a measurable Quench Phase Shift (QPS), Φq, in the sensor qubit coherence, which is uniquely sensitive to the environment’s dissipative response properties (spectral function J[ω]).
- Direct Temperature Measurement: For Ohmic environments in thermal equilibrium, the QPS enables the direct, curve-fitting-free measurement of the environmental temperature (KBT) using only the measured T2 decoherence time and the asymptotic QPS value.
- Diagnosis of Non-Equilibrium States: By comparing the fluctuation properties (Noise Spectral Density, S[ω]) and the response properties (J[ω]), the protocol can diagnose if the bath is in a non-thermal equilibrium state (i.e., if the effective temperature Teff[ω] is frequency-dependent).
- Spectral Function Reconstruction: Utilizing multi-level sensor systems (like diamond NV centers), researchers can engineer complex, time-dependent quenches to reconstruct the full spectral function J[ω] over a broad frequency range, analogous to how S[ω] is reconstructed in conventional QNS.
- General Applicability: The underlying quench physics is shown to be intrinsic to a wide range of T2-type protocols and is applicable to both Gaussian quantum baths (e.g., phononic/photonic modes) and, via linear response approximation, to non-Gaussian environments.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Qubit Coherence Function | (1/2) e-S(tf) e-iΦ(tf) | Dimensionless | Magnitude (S) and Phase (Φ) of coherence |
| Direct Thermometry (Ohmic) | KBT = 1 / (2T2 Φq(∞)) | Energy/Temperature | Requires Hahn-echo T2 and asymptotic QPS (no curve fitting) |
| Low-Frequency NSD Scaling | S[ω] ~ S0ωp | Frequency dependence | Noise Spectral Density (NSD) power law exponent p |
| Low-Frequency Response Scaling | J[ω] ~ A0ωs/π | Frequency dependence | Spectral Function (DOS) power law exponent s |
| Ohmic Bath Exponents | p = 0, s = 1 | Dimensionless | Standard low-frequency behavior |
| 1/f Noise Exponents | p = -1, s = 0 | Dimensionless | Standard low-frequency behavior |
| QPS Long-Time Scaling | Φq(tf) ~ tf-s | Time dependence | Asymptotic behavior for protocol time tf → +∞ |
| QPS Validity Range (s) | -2 < s < 2 | Dimensionless | Range for universal asymptotic QPS behavior |
| Dephasing Validity Range (p) | -3 < p < 1 | Dimensionless | Range for universal asymptotic dephasing behavior |
Key Methodologies
Section titled “Key Methodologies”- Qubit Initialization and Quench Induction: The sensor qubit is initialized in a pure state (e.g., |↓>) unentangled with the bath. An instantaneous π/2-pulse prepares the qubit in a superposition state (|+>), which instantaneously changes the effective bath Hamiltonian (Hb,eff), thereby inducing the quantum quench.
- T2-Type Protocol Execution: The system evolves under the total Hamiltonian Htot for time tf, interspersed with standard control π-pulses (e.g., Ramsey, Hahn echo, or Dynamical Decoupling sequences) to mitigate low-frequency noise.
- Coherence Measurement: The qubit coherence, characterized by its magnitude (dephasing function S(tf)) and phase shift (Φ(tf)), is measured by repeating the protocol and measuring Pauli operators (σx, σy).
- Quench Phase Shift (QPS) Isolation: The QPS (Φq) is isolated from the total phase shift. This is possible because Φq is uniquely sensitive to the initial state of the qubit (before the π/2-pulse), unlike phase shifts caused by external ambient fields (Φext).
- Response Function Extraction (Linear Response): In the weak coupling or Gaussian limit, the QPS is directly related to the imaginary part of the retarded Green’s function (ImGRξV[ω]), which is proportional to the environmental spectral function J[ω] (effective density of states).
- Engineered Time-Dependent Quenches (NV Centers): To reconstruct J[ω] over a broad frequency range, a multi-level sensor (like an NV center spin-1 system) is used. The quench function η(t) is actively modulated by periodically switching the sensor spin between different qubit subspaces (e.g., {mz = 0, mz = -1} and {mz = 0, mz = +1}) during the protocol. This generates a frequency-comb filter for J[ω].
Commercial Applications
Section titled “Commercial Applications”| Industry/Field | Application/Product | Technical Relevance |
|---|---|---|
| Quantum Computing | Qubit Decoherence Mitigation | Provides independent characterization of both noise (S[ω]) and dissipation (J[ω]) in superconducting or spin qubit environments, crucial for optimizing coherence times. |
| Quantum Sensing (NV Centers) | Enhanced Magnetic/Electric Field Sensing | Utilizes the NV center’s spin-1 structure to engineer complex quenches, allowing for full spectral reconstruction of magnetic noise sources (e.g., nuclear spins). |
| Materials Science | Characterization of Quantum Materials | Direct measurement of the effective density of states (J[ω]) and dissipative susceptibility, which are fundamental properties of correlated electron systems and novel quantum materials. |
| Cryogenic Engineering | Non-Invasive Thermometry | Enables direct, in-situ measurement of the environmental temperature (KBT) in cryogenic quantum devices without relying on complex curve fitting, especially valuable for Ohmic baths. |
| Fundamental Metrology | Probing Non-Gaussian Noise | The quench formalism provides a pathway to access higher-order nonlinear response functions and noise susceptibilities, moving beyond the Gaussian approximation for complex environments. |
View Original Abstract
We discuss how standard $T_2$-based quantum sensing and noise spectroscopy\nprotocols often give rise to an inadvertent quench of the system or environment\nbeing probed: there is an effective sudden change in the environmental\nHamiltonian at the start of the sensing protocol. These quenches are extremely\nsensitive to the initial environmental state, and lead to observable changes in\nthe sensor qubit evolution. We show how these new features can be used to\ndirectly access environmental response properties. This enables methods for\ndirect measurement of bath temperature, and methods to diagnose non-thermal\nequilibrium states. We also discuss techniques that allow one to deliberately\ncontrol and modulate this quench physics, which enables reconstruction of the\nbath spectral function. Extensions to non-Gaussian quantum baths are also\ndiscussed, as is the direct applicability of our ideas to standard diamond\nNV-center based quantum sensing platforms.\n