Possibility of Direct Observation of the Bloch—Siegert Shift in Coherent Dynamics of Multiphoton Raman Transitions
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2019-10-01 |
| Journal | Journal of Experimental and Theoretical Physics Letters |
| 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 | 3 |
| Analysis | Full AI Review Included |
6CCVD Technical Documentation: The Direct Observation of the Bloch-Siegert Shift in Diamond NV Centers
Section titled “6CCVD Technical Documentation: The Direct Observation of the Bloch-Siegert Shift in Diamond NV Centers”This technical documentation analyzes the research detailing coherent dynamics in solid-state quantum systems, specifically focusing on the critical role of high-purity diamond substrates for realizing ultrastrong coupling regimes necessary for observing the Bloch-Siegert shift ($\omega_{BS}$). This work provides a foundation for advanced quantum control techniques, directly leveraging 6CCVD’s expertise in engineered MPCVD diamond materials.
Executive Summary
Section titled “Executive Summary”The analyzed research proposes a method for the direct observation of the Bloch-Siegert shift ($\omega_{BS}$) in the time-resolved coherent dynamics of a qubit system, using parameters applicable to Nitrogen-Vacancy (NV) centers in diamond.
- Application Focus: Demonstrates advanced coherent control of qubits operating in the ultrastrong coupling regime ($g/\epsilon \approx 0.8$) via second-order multiphoton Raman transitions.
- Key Achievement: Theoretical proposal showing how to suppress the Rotating Wave Approximation (RWA) Rabi frequency ($\Omega_{2}$) via destructive interference of multiphoton processes.
- Isolation Technique: By tuning the normalized low-frequency amplitude ($A/\omega$) to a specific critical value ($A^*/\omega \approx 2.68$), the BSS oscillation is isolated with constant amplitude, allowing for direct measurement.
- Spectral Manifestation: The isolation transforms characteristic Fourier spectral triplets (observed during standard Rabi oscillations) into clear doublets, with the splitting precisely equaling $2\omega_{BS}$.
- Material Relevance: The methodology is based on experimental conditions realized using solid-state spin systems, making high-purity, low-strain SCD diamond substrates essential for replication and extension.
- Significance: Offers a powerful new technique for studying driven quantum systems under bichromatic or multichromatic control in the deep ultrastrong regime.
Technical Specifications
Section titled “Technical Specifications”The following parameters, based on calculations modeling NV centers in diamond, define the experimental conditions for achieving BSS isolation and direct observation:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Qubit System | NV Center | N/A | Solid-state spin system in high-purity diamond |
| Coupling Regime | Ultrastrong | $g/\epsilon$ | Defined by $A \cos\theta/\omega \approx 0.8$ |
| Coherence Time ($\tau$) | 4 | µs | Phenomenologically introduced for decay rate $\gamma$ |
| Low-Frequency Driving ($\omega/2\pi$) | 5.22 | MHz | Amplitude modulation frequency |
| High-Frequency Detuning ($\Delta_x/2\pi$) | 10 | MHz | Microwave field detuning |
| Qubit Detuning ($\Delta_z/2\pi$) | 3 | MHz | Transition energy detuning |
| Critical Normalized Amplitude ($A^*/\omega$) | 2.68 | N/A | Amplitude ratio where $\Omega_{2} = 0$ due to destructive interference |
| Observed Spectral Signature | $2\omega_{BS}$ | Frequency | Doublet splitting reveals twice the Bloch-Siegert shift |
| Spin States Studied | $ | 0\rangle$ and $ | -1\rangle$ |
Key Methodologies
Section titled “Key Methodologies”The theoretical approach utilized the semiclassical Rabi model combined with non-secular perturbation theory to accurately capture the dynamics in the ultrastrong regime beyond the limitations of the standard Rotating Wave Approximation (RWA).
- Hamiltonian Formulation: The system starts with the lab-frame Hamiltonian ($H_{lab}$) describing a two-level qubit driven by an amplitude-modulated bichromatic microwave field.
- Frame Transformations: Successive transformations (rotating frame and canonical transformations) were applied to decouple fast oscillations and isolate the relevant dynamics in the $H_{2}$ Hamiltonian.
- Non-RWA Effective Hamiltonian: The Bogoliubov averaging method was used to construct a time-independent effective Hamiltonian ($H_{eff} = H_{2}^{(1)} + H_{2}^{(2)}$), including contributions up to the second order to incorporate counter-rotating (non-RWA) terms.
- Rabi Frequency Components: $H_{eff}$ yielded a RWA Rabi frequency ($\Omega_{2}$) based on Bessel functions $J_{2}(a)$, and the Bloch-Siegert frequency shift ($\omega_{BS}^{BS}$) generated by non-resonant oscillating terms.
- Isolation Condition: The critical normalized amplitude $A^*/\omega$ was identified as the first root of $J_{2}(a) = 0$. At this point, $\Omega_{2}$ vanishes due to destructive multiphoton interference.
- Dynamics Analysis: Qubit ground state population $P^{(2)}(t)$ was calculated under the isolation condition, demonstrating the emergence of the constant-amplitude Bloch-Siegert oscillation $\omega_{BS}^{BS}$ exclusively.
- Spectral Verification: Fourier spectra of the dynamics $F(\omega)$ were analyzed to confirm the transition from characteristic triplets (containing $\Omega_{2}$ and $\omega_{BS}^{BS}$) to pure doublets (split by $2\omega_{BS}^{BS}$).
6CCVD Solutions & Capabilities
Section titled “6CCVD Solutions & Capabilities”The successful replication and extension of this research relies fundamentally on ultra-high-quality diamond substrates, specifically optimized for long spin coherence and precise device integration. 6CCVD, as an expert MPCVD diamond manufacturer, offers tailored solutions to meet these demanding requirements.
Applicable Materials for Quantum Control
Section titled “Applicable Materials for Quantum Control”NV center experiments require the highest available quality single-crystal diamond (SCD) to minimize defects, nitrogen concentration, and strain, which are primary factors limiting coherence time (4 µs in the modeled case).
| 6CCVD Material Solution | Specifications | Application Context |
|---|---|---|
| Optical Grade SCD | Nitrogen < 1 ppb (Type IIa) | Ideal for NV center creation and manipulation, ensuring maximum spin coherence time ($\tau$). |
| Custom Thickness SCD | 0.1 µm - 500 µm | Enables precise waveguide coupling and creation of shallow NVs for surface microwave interaction. |
| Substrate Thickness | Up to 10 mm | Provides robust mechanical support and efficient heat sinking for high-power microwave components. |
Customization Potential & Device Integration
Section titled “Customization Potential & Device Integration”Realizing the ultrastrong driving regime requires integrating complex microwave structures directly onto the diamond surface to generate the precise bichromatic fields.
- Advanced Polishing: The stability and reliability of NV centers close to the surface depend critically on surface roughness. 6CCVD guarantees Ra < 1 nm polishing for SCD wafers, optimizing the surface interface for nanofabrication and quantum coherence.
- Custom Dimensions: We provide custom-sized plates and wafers up to 125 mm (PCD) or application-specific dimensions for SCD, allowing researchers to integrate diamonds seamlessly into existing cryostats or microwave circuitry.
- In-House Metalization Services: The generation of local, high-power amplitude-modulated fields often requires custom antenna or strip-line fabrication. 6CCVD offers internal, high-precision metalization capabilities, including deposition of:
- Adhesion Layers: Ti, W
- Conductive Layers: Au, Cu
- Robust Contacts: Pt, Pd
- Laser Cutting and Shaping: To facilitate integration into microwave packages, 6CCVD offers custom laser cutting services for precise wafer shaping and clean dicing without compromising material integrity.
Engineering Support
Section titled “Engineering Support”6CCVD’s in-house PhD material science team can assist with material selection for similar driven quantum system (Floquet Engineering) projects. We specialize in optimizing diamond growth parameters to achieve specific goals, such as maximizing coherence time, controlling NV density, or engineering substrate properties for high-frequency applications.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. Global shipping (DDU default, DDP available) ensures prompt delivery of mission-critical materials worldwide.
View Original Abstract
We study Rabi oscillations of the second-order Raman transition realized on\ndressed states of a qubit excited by an amplitude-modulated microwave field.\nThe co-rotating component of the ultrastrong low-frequency modulation field\nexcites virtual multiple photon processes between the dressed states and forms\nthe Rabi frequency in the so-called rotating wave approximation (RWA). The\ncounter-rotating modulation component also gives a significant contribution to\nthe Rabi frequency owing to the Bloch—Siegert effect. It is shown that for\nproperly chosen parameters of the modulation field and qubit, the Rabi\noscillations in the RWA vanish due to destructive interference of multiple\nphoton processes. In this case the Rabi oscillation results exclusively from\nthe Bloch—Siegert effect and is directly observed in the time-resolved\ncoherent dynamics as the Bloch—Siegert oscillation. Correspondingly, in\nFourier spectra of the coherent response, triplets are transformed into\ndoublets with the splitting between the lines equal to twice the Bloch—Siegert\nshift. We demonstrate these features by calculations of the qubit’s evolution\nin the conditions of experiments with a NV center in diamond, where Raman\ntransitions were observed. The direct observation of the Bloch—Siegert\noscillation offers new possibilities for studying driven quantum systems in the\nultastrong regime.\n
Tech Support
Section titled “Tech Support”Original Source
Section titled “Original Source”References
Section titled “References”- 2016 - Electron Spin Resonance Based Quantum Computing [Crossref]
- 1992 - Atom—Photon Interactions: Basic Processes and Applications