Bloch–Siegert oscillations in the Rabi model with an amplitude-modulated driving field
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2019-10-23 |
| Journal | Laser Physics |
| Authors | A. P. Saiko, S.A. MARKEVICH, R. Fedaruk, A. P. Saiko, S.A. MARKEVICH |
| Institutions | University of Szczecin, National Academy of Sciences of Belarus |
| Citations | 7 |
| Analysis | Full AI Review Included |
Technical Analysis and Documentation for 6CCVD
Section titled “Technical Analysis and Documentation for 6CCVD”Executive Summary
Section titled “Executive Summary”The analyzed research details a novel method for the direct observation and measurement of the Bloch-Siegert (BS) shift ($\omega^{\text{BS}}$) in two-level quantum systems operating in the ultrastrong coupling (USC) regime, using an amplitude-modulated microwave field. This technique is specifically proposed for implementation using Nitrogen Vacancy (NV) centers in diamond, directly linking the findings to 6CCVD’s core MPCVD Single Crystal Diamond (SCD) capabilities.
- Core Achievement: Demonstration of a technique to isolate the Bloch-Siegert oscillation ($\omega^{\text{BS}}$) from complex multiphoton coherent dynamics.
- Physical Mechanism: Destructive interference of multiple photon processes at the Rabi resonance forces the RWA Rabi frequency ($\Omega$) to vanish, leaving the dynamics dominated by the BS shift.
- Material Focus: The experiment relies on the coherent spin dynamics of the NV center in solid-state Single Crystal Diamond (SCD).
- Spectral Signature: The key observable is the transformation of the Fourier spectrum response from a series of triplets into characteristic doublets, where the splitting is precisely $2\omega^{\text{BS}}$.
- Operational Regime: Requires operation in the ultrastrong coupling regime, characterized by a coupling constant $A \text{cos} \theta / \omega \approx 0.57$.
- Application Relevance: Provides a critical new technique for precision measurement and coherent control of spin qubits, highly valuable for quantum information processing and quantum sensing applications.
Technical Specifications
Section titled “Technical Specifications”The following parameters were utilized in the theoretical model, simulating conditions achievable in NV center diamond experiments:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Low-Frequency Modulation ($\omega$) / 2$\pi$ | 10.44 | MHz | Primary driving field modulation frequency |
| High-Frequency Detuning ($\Delta_{\text{x}}$) / 2$\pi$ | 10 | MHz | Field relative detuning parameter |
| Qubit Detuning ($\Delta_{\text{z}}$) / 2$\pi$ | 3 | MHz | Energy transition parameter |
| Coherence Time ($\tau$) | 4 | µs | Phenomenological decay time used for Fourier analysis |
| Ultrastrong Coupling Constant ($A \text{cos} \theta / \omega$) | $\approx 0.57$ | - | Regime necessary for significant non-RWA effects |
| Rabi Resonance Condition ($A^{*} / \omega$) | 2.00 | - | Low-frequency amplitude value where $\Omega=0$ |
| Bloch-Siegert Shift ($\omega_{\nu}$) / 2$\pi$ | 20.9 | MHz | Example maximum shift observed in the second triplet |
| Observable Splitting (Doublet) | $2\omega^{\text{BS}}$ | MHz | Used for direct measurement of the BS shift |
Key Methodologies
Section titled “Key Methodologies”The theoretical framework proposes an advanced coherent spectroscopy technique based on the precise manipulation of energy levels in the ultrastrong coupling regime:
- Qubit System Selection: Utilizing a two-level spin qubit system (e.g., NV center $|0\rangle$ and $|-1\rangle$ sublevels) initially prepared in the ground state $|0\rangle$.
- Bichromatic Driving Field: Excitation using an amplitude-modulated microwave field $V(t)$, comprising high- and low-frequency components ($\omega_{1}$ and $\omega$) to induce complex coherent dynamics.
- Frame Transformations: Applying sequential rotating frame transformations and canonical transformations to simplify the interaction Hamiltonian ($H \rightarrow H_{1} \rightarrow H_{2}$).
- Effective Hamiltonian Derivation: Employing the Bogoliubov averaging method (up to the second order) to construct a time-independent effective Hamiltonian ($H_{\text{eff}}$), accounting for non-secular (non-RWA) terms.
- Rabi Resonance Tuning: Precisely tuning the low-frequency amplitude ($A$) such that the RWA Rabi frequency ($\Omega$) vanishes due to destructive interference of multiphoton processes ($A = A^{*}$, where $J_{1}(a)=0$).
- Direct Observation: Monitoring the time-resolved evolution of the ground state population $P_{|0\rangle}(t)$, which, at the tuned resonance, exhibits pure Bloch-Siegert oscillations ($\Omega^{*} = \omega^{\text{BS}}$).
- Spectral Analysis: Analyzing the Fourier spectrum of $P_{|0\rangle}(t)$ to confirm the transformation of multiphoton triplets ($n\omega \pm \Omega^*$) into doublets ($n\omega \pm \omega^{\text{BS}}$), allowing the direct determination of $2\omega^{\text{BS}}$.
6CCVD Solutions & Capabilities
Section titled “6CCVD Solutions & Capabilities”The replication and advancement of this cutting-edge quantum research—focused on NV centers and ultrastrong coupling—depend critically on the quality and customization of the underlying diamond material. 6CCVD provides the necessary engineered MPCVD diamond solutions to support this highly technical field.
| Requirement from Paper (NV Research) | 6CCVD Material/Solution | Technical Specification Match |
|---|---|---|
| High Coherence Time (4 µs stated) | Optical Grade Single Crystal Diamond (SCD) | Our high-purity SCD is optimized for low residual nitrogen concentration (< 1 ppb possible) to maximize $T_{2}$ coherence and facilitate optimal NV formation/isolation. |
| Qubit Integration & Device Fabrication | Custom Dimensions & Thickness Control | We offer SCD materials in thicknesses ranging from 0.1 µm to 500 µm. Crucial for thin film quantum devices and integrated photonics. |
| Surface Criticality (NV Proximity) | Ultra-Smooth Polishing | Our proprietary polishing capabilities guarantee surface roughness of Ra < 1 nm for SCD wafers, essential for minimizing surface noise and preserving qubit coherence near the surface. |
| Microwave Delivery Structure | In-House Custom Metalization Services | We provide internal metalization layering including Au, Pt, Pd, Ti, W, and Cu. This is vital for depositing co-planar waveguides or antennas required to deliver the amplitude-modulated microwave field (USC regime). |
| Reproducibility & Scalability | Large Format Capability | While NV research often uses smaller samples, 6CCVD can produce high-quality PCD plates up to 125 mm, ensuring scalability of future quantum integrated circuits. |
Applicable Materials
Section titled “Applicable Materials”To replicate or extend this research utilizing NV centers for direct Bloch-Siegert shift measurement, the following 6CCVD material is essential:
- Optical Grade Single Crystal Diamond (SCD): Required due to the need for high lattice purity and low defects/impurities to support long coherence times ($\tau$). The quality must support controlled creation and manipulation of NV centers.
Customization Potential
Section titled “Customization Potential”The utilization of an amplitude-modulated microwave field often requires integration with patterned metal structures on the diamond surface.
- 6CCVD offers extensive custom metalization capabilities, allowing researchers to define complex Ti/Pt/Au or other multilayer stacks for efficient microwave delivery into the USC regime.
- We provide precision laser cutting and shaping to deliver custom geometry plates and wafers required for mounting in specialized cryogenic or microwave spectroscopy setups.
Engineering Support
Section titled “Engineering Support”Understanding the complex interplay between qubit dynamics (Rabi oscillations, Bloch-Siegert effects) and material properties (nitrogen concentration, defect density) is crucial. 6CCVD’s in-house PhD-level engineering team specializes in MPCVD diamond properties for quantum applications. We can assist researchers with material selection, thickness optimization, and surface preparation specifications specifically tailored for similar Solid-State Spin Qubit Coherent Control projects.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
We study the coherent dynamics of a qubit excited by an amplitude-modulated\nelectromagnetic field under the Rabi resonance when the frequency of the\nlow-frequency modulation field matches the Rabi frequency in the high-frequency\nfield. Due to destructive interference of multiple photon processes at the\nultrastrong coupling between the qubit and the low-frequency driving field,\nRabi oscillations result exclusively from the Bloch-Siegert effect. It is\ndirectly observed in the time-resolved coherent dynamics as the Bloch-Siegert\noscillation. In this case, triplets in Fourier spectra of the coherent response\nare transformed into doublets with the splitting between the lines equal to\ntwice the Bloch-Siegert shift. These unusual properties are demonstrated in\nconditions of experiments with a nitrogen vacancy center in diamond.\n