Cooperative Light Emission in the Presence of Strong Inhomogeneous Broadening
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2019-09-20 |
| Journal | Physical Review Letters |
| Authors | Chen Sun, Vladimir Chernyak, Andrei Piryatinski, Nikolai A. Sinitsyn |
| Institutions | Los Alamos National Laboratory, Wayne State University |
| Citations | 12 |
| Analysis | Full AI Review Included |
Technical Analysis and Material Sourcing for Cooperative Diamond Emitters
Section titled âTechnical Analysis and Material Sourcing for Cooperative Diamond EmittersâExecutive Summary
Section titled âExecutive SummaryâThis analysis focuses on the feasibility and material requirements for replicating and extending the demonstrated dynamic phase transition in cooperative light emission, specifically using negatively charged Nitrogen-Vacancy (NV-) centers embedded in synthetic diamond.
- Core Achievement: Observation of a sharp phase transition in cooperative light emission behavior, dictated by the photonic cavity frequency sweeping rate ($\beta$).
- Mechanism: A linear frequency chirp protocol allows an ensemble of NV centers to transition discontinuously from a weak to a strong cooperative emission phase, effectively releasing stored spin energy as a pulse of coherent radiation.
- Material Mandate: Experimental realization requires ultra-high purity Single Crystal Diamond (SCD) to host high concentrations of NV centers ($N \sim 10^8$ to $10^{12}$) while maintaining long quantum coherence times ($T_2 \sim 1$ ms).
- Critical Requirement: To observe the transition before decoherence, the system must utilize a high-quality (Q) microwave cavity, requiring $Q \ge 10^6$.
- 6CCVD Value Proposition: 6CCVD provides the necessary Electronic/Optical Grade SCD material, optimized for high $T_2$ and low strain, along with crucial custom engineering services (precision polishing and metalization) essential for seamless integration into high-Q microwave circuits (Circuit QED).
- Application: This research enables the design of solid-state microstructures for on-demand coherent light pulsing and localized information exchange within quantum circuits.
Technical Specifications
Section titled âTechnical SpecificationsâThe following table summarizes the key physical parameters and conditions necessary to observe the dynamic phase transition, directly connecting experimental requirements to material specifications.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Material Host | NV- Centers in Diamond | N/A | Essential two-level spin system. |
| Spin Ensemble Size (N) | $6 \times 10^8$ to $10^{12}$ | Defects | Minimum required for transition observability. |
| Cavity Type | Half-Wavelength Microwave | N/A | Must be piezoelectrically tunable over 1 GHz range. |
| Spin-Boson Coupling ($g_k$) | 10 | Hz | Typical coupling strength for NV centers [8]. |
| Spin Coherence Time ($T_2$) | $\ge 1$ | ms | Must exceed the photon lifetime $t_L \sim 0.3 \times 10^{-3}$ sec. |
| Spin Relaxation Time ($T_1$) | Hours | N/A | Achievable at cryogenic temperatures, far off-resonance. |
| Inhomogeneous Broadening | $\sim 3$ | MHz | Standard deviation $\sqrt{\text{var}(\epsilon_k)}$ for NV centers. |
| Critical Sweeping Rate ($\beta_c$) | $2\pi g^2 N / \log_e N$ | [Energy]2 | Phase transition control parameter. Value $\sim 10^4$ MHz/sec for $N \sim 10^8$. |
| Minimum Quality Factor (Q) | $10^6$ | Unitless | Required for the collective emission condition (Eq. 11). |
| Emission Time ($t_L$) | $0.3 \times 10^{-3}$ | sec | Duration of the coherent photon pulse emitted. |
Key Methodologies
Section titled âKey MethodologiesâThe experiment relies on precise control over the cavity environment and the synchronization of the frequency sweep protocol with the quantum system dynamics.
- NV Center Preparation: Utilize high-purity Single Crystal Diamond (SCD) containing a dense ensemble of negatively charged NV centers (NV-). NV density must be controlled to meet $N_{\text{min}} \approx 6 \times 10^8$.
- Microwave Cavity Coupling: Integrate the diamond material into a half-wavelength microwave cavity. The cavity must provide a high Quality factor ($Q \ge 10^6$).
- Tunability Implementation: Employ a piezoelectric mechanism to linearly sweep the cavity frequency $\omega(t)$ over a range of $\sim 1$ GHz.
- Initial Spin Polarization: Induce an initial, fully âupâ polarized spin state (spin excitation ground state) using established optical initialization protocols.
- Linear Frequency Chirp Protocol: Apply the cavity frequency modulation $\omega(t) = \langle\epsilon_k\rangle - \beta t$. The modulation must span the full inhomogeneous broadening range, $\pm \beta T > \sqrt{\text{var}(\epsilon_k)}$.
- Critical Tuning: Adjust the sweeping rate $\beta$ to identify the critical point $\beta_c$. Observation requires operating in the âslowâ regime ($\beta < \beta_c$), where the majority of spins cooperatively emit photons.
- Observation Constraint: The total sweep time $2T \sim 10^{-4}$ sec must be significantly shorter than the spin coherence time ($T_2 \sim 1$ ms) and must satisfy the constraint for observable collective emission (Eq. 11): $\bar{\epsilon}_k \sqrt{\text{var}(\epsilon_k)} \log_e N / (\pi Q g^2 N) < 1$.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & Capabilitiesâ6CCVD offers the essential high-performance diamond components and fabrication services required to successfully implement this advanced quantum control protocol, particularly focusing on mitigating decoherence and optimizing integration into circuit QED systems.
Applicable Materials
Section titled âApplicable MaterialsâThe rigorous requirement for long coherence times ($T_2$) and minimal strain dictates the use of 6CCVDâs premium SCD materials:
| Research Requirement | 6CCVD Material Solution | Optimization Feature |
|---|---|---|
| High $T_2$ and $T_1$ | Electronic Grade Single Crystal Diamond (SCD) | Ultra-low concentration of residual nitrogen and point defects, reducing phonon-induced decoherence. |
| Dense Spin Ensemble | SCD with Controlled Doping | Precise control over MPCVD growth parameters allows for the targeted incorporation of NV precursor elements (e.g., nitrogen) to achieve the high $N$ density ($10^8$ to $10^{12}$) required. |
| Optical Interfaces | Optical Grade SCD | High transmission across relevant microwave and optical ranges for initialization and measurement processes. |
| Piezoelectric Integration | Boron-Doped Diamond (BDD) (Optional) | For potential integration of conductive electrodes directly onto the diamond surface for electric field manipulation of spin splittings, BDD provides a highly stable platform. |
Customization Potential
Section titled âCustomization PotentialâExperimental success hinges on precise diamond geometry and interface quality for effective cavity coupling. 6CCVD offers full customization to meet stringent quantum engineering needs:
- Dimensional Control: The integration into a microwave cavity requires custom dimensions and shapes. 6CCVD delivers custom laser-cut diamond plates and wafers up to 125 mm (PCD) or precision-cut SCD samples in arbitrary geometries (e.g., microdisks, trapezoids) tailored for specific half-wavelength microwave designs.
- Surface Quality: Achieving high-Q coupling necessitates minimal surface roughness. 6CCVD guarantees ultra-smooth polishing (Ra < 1 nm for SCD), critical for reducing scattering losses and interface defects that lead to decoherence.
- Interface Metalization: For integrating contacts to piezoelectric tuning elements or superconducting circuit elements (Circuit QED), 6CCVD provides in-house metalization services, including common high-conductivity and stable adhesion stacks such as Ti/Pt/Au, Ti/W, or Cu.
Engineering Support
Section titled âEngineering SupportâThe complexity of controlling NV density, maximizing $T_2$, and ensuring compatibility with high-Q cryogenic systems demands expert guidance.
- 6CCVDâs in-house PhD engineering team specializes in MPCVD growth recipes tailored for quantum applications. We can assist researchers in selecting the optimal diamond substrate orientation and nitrogen concentration profile necessary to replicate or extend this research on Cooperative Light Emission and Dynamic Phase Transitions.
- Our technical consultants provide detailed specifications on thermal management, mechanical stability, and chemical compatibility essential for cryogenically-cooled circuit QED experiments.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
We study photon emission by an ensemble of two-level systems, with strong inhomogeneous broadening and coupled to a cavity mode whose frequency has linear time dependence. The analysis shows that, regardless of the distribution of energy level splittings, a sharp phase transition occurs between the weak and strong cooperative emission phases near a critical photonic frequency sweeping rate. The associated scaling exponent is determined. We suggest that this phase transition can be observed in an ensemble of negatively charged NV^{-} centers in diamond interacting with a microwave half-wavelength cavity mode even in the regime of weak coupling and at strong disorder of two-level splittings.