Single and two-mode mechanical squeezing of an optically levitated nanodiamond via dressed-state coherence
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2016-10-03 |
| Journal | New Journal of Physics |
| Authors | Wenchao Ge, M. Bhattacharya |
| Institutions | Rochester Institute of Technology |
| Citations | 17 |
| Analysis | Full AI Review Included |
Technical Documentation: Quantum State Engineering in Levitated Nanodiamonds
Section titled âTechnical Documentation: Quantum State Engineering in Levitated NanodiamondsâInternal Document Ref: NJP-18-103002 Analysis | 6CCVD Quantum Applications
Executive Summary
Section titled âExecutive SummaryâThis paper presents a novel, experimentally feasible method for achieving single- and two-mode mechanical squeezing of an optically levitated nanodiamond containing a single Nitrogen-Vacancy (NV) center. The findings are highly relevant to quantum metrology and solid-state quantum mechanics.
- Core Achievement: Demonstrated theoretical feasibility of generating steady-state quantum mechanical squeezing in a cavity-free spin-optomechanical system.
- Material Basis: Utilizes an optically levitated nanodiamond (50 nm radius) containing a single NV electron spin.
- Key Mechanism: Mechanical motion is coupled to the NV spin via a magnetic field gradient. Two microwave fields create a dressed three-level system, inducing a two-phonon transition essential for squeezing.
- Feasibility under Real Conditions: Quantum squeezing is achievable at room temperature, provided state-of-the-art techniquesâspecifically ultrahigh vacuum (< $10^{-8}$ mbar) and strong feedback cooling (reducing initial phonon number $n_{th}$ to $\sim 2$)âare employed.
- Performance Metrics: Calculations show the possibility of strong quantum squeezing, exceeding the 3 dB limit.
- Scalability: The scheme is readily extendable to two-mode squeezing using appropriate magnetic field gradients, useful for sensitive phase measurement.
- 6CCVD Relevance: Requires ultra-high purity, high-coherence diamond material (SCD) as a precursor for reliable NV center incorporation and processing.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points define the requirements and operational parameters for realizing quantum squeezing in the levitated nanodiamond system.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Nanodiamond Radius | 50 | nm | Size used for calculations |
| Mechanical Oscillation Frequency ($\omega_{m}/2\pi$) | 1.0 | MHz | Typical frequency of the harmonic trap |
| Mechanical Quality Factor (Q) | $10^{6}$ | Unitless | Required Q for strong squeezing |
| Initial Mean Phonon Number ($n_{th}$) | $10^{3}$ | Unitless | Baseline at room temperature |
| Target Mean Phonon Number ($n_{th}$) | $\sim 2$ | Unitless | Required for quantum squeezing with feedback cooling |
| Required Vacuum Level | < $10^{-8}$ | mbar | Ultrahigh Vacuum (UHV) required for low damping |
| Gas Damping Rate ($\gamma_m / 2\pi$) | $\sim 10^{-6}$ | Hz | Achievable in UHV |
| Required Magnetic Field Gradient | $\sim 10^{5}$ | T m$^{-1}$ | Used for mechanical-spin coupling |
| Optical Pump Rabi Frequency ($\Omega_{p}$) | $\sim 8$ | MHz | Used to induce fast spin dissipation |
| Excited State Decay Rate ($\gamma_{e}$) | $\sim 40$ | MHz | Typical decay rate for NV excited states |
| Quantum Squeezing Target | $\text{(}\Delta x\text{)}^{2} - 1/4 < -1/8$ | Unitless | Demonstrates squeezing beyond the 3 dB limit |
Key Methodologies
Section titled âKey MethodologiesâThe experiment relies on engineering a specific set of interactions between the NV center spin and the mechanical oscillator (phonon modes) using externally applied electromagnetic fields.
- Preparation and Trapping: A nanodiamond containing a single NV center is optically levitated in an Ultrahigh Vacuum (UHV) environment to minimize mechanical damping ($\gamma_m$). Feedback cooling is applied to reduce the mean phonon occupation number ($n_{th}$) close to the ground state.
- Spin-Mechanical Coupling: A strong, localized magnetic field gradient ($\sim 10^{5}$ T m$^{-1}$) is applied, coupling the center-of-mass motion (phonon annihilation/creation operators $d, d^{\dagger}$) to the NV electron spin operator ($S_{z}$).
- Dressed-State Initialization: Two microwave fields, defined by Rabi frequencies $\Omega_{0}$ and $\Omega_{1}$, are applied to couple the NV center ground states ($|0\rangle$ and $|\pm 1\rangle$), creating a system of dressed states ($|a\rangle, |b\rangle, |c\rangle$).
- Dissipation and Coherence: Two optical fields with Rabi frequency $\Omega_{p}$ drive the ground states to the excited states ($|E_{1}\rangle, |E_{2}\rangle$), inducing rapid, state-selective spin dissipation ($\gamma_{0}, \gamma_{1}$). This dissipation is crucial for generating steady-state mechanical squeezing and coherence.
- Resonant Tuning: The system parameters (detunings $\Delta$, $\Omega_{0}$, $\Omega_{1}$) are tuned to ensure that the mechanical frequency ($\omega_{m}$) is resonant with the transition frequency between the dressed states $|b\rangle$ and $|c\rangle$, facilitating the necessary two-phonon transition.
- Two-Mode Extension: To achieve two-mode squeezing, the magnetic field gradient is applied in both X and Y directions, coupling two independent mechanical modes to the single NV spin, requiring fine control over the field gradients to suppress unwanted spin coupling ($S_{x}$).
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâReplicating or advancing this quantum state engineering research requires diamond materials with exceptional purity and precise physical characteristics. 6CCVD specializes in providing the MPCVD substrates necessary for producing high-coherence NV centers and the custom processing required for integration into quantum systems.
Applicable Materials
Section titled âApplicable Materialsâ| Research Requirement | 6CCVD Material Specification | Rationale for Selection |
|---|---|---|
| Precursor for NV Generation: High crystal quality, low strain necessary for stable, high-coherence NV electron spins. | Optical Grade Single Crystal Diamond (SCD): High-purity MPCVD-grown material (low background Nitrogen). | SCD wafers are the standard substrate for creating predictable, high-coherence NV centers via controlled doping or ion implantation, crucial for achieving long spin coherence times (up to 1 ms at 300 K). |
| Substrate for Fabrication: Robust, large-area substrate for supporting the complex microwave/optical circuits and magnetic tips necessary for coupling. | Polycrystalline Diamond (PCD): Wafers up to 125mm with high thermal conductivity. | Excellent heat dissipation and mechanical stability for co-locating high-power optical/microwave components adjacent to the NV nanodiamond. |
| Material Doping Control: Potential future need for conductive diamond sensors or gates. | Boron-Doped Diamond (BDD): Customizable doping levels (p-type conductivity). | Allows for in-situ integration of highly stable electrochemical sensors or solid-state gates into the quantum mechanical platform. |
Customization Potential for Replication & Advancement
Section titled âCustomization Potential for Replication & AdvancementâThe levitated nanodiamond experiment requires specialized dimensions and component integration, areas where 6CCVDâs full-service engineering capabilities provide crucial support.
- Precision Precursor Sizing: While the final active material is a 50 nm nanodiamond, the precursor SCD wafer must be processed (e.g., via etching or slicing) to yield the nanostructures. 6CCVD offers custom SCD plates and wafers in thicknesses optimized for efficient exfoliation or etching (0.1 ”m - 500 ”m).
- Optical Surface Quality: Successful optical levitation relies on minimal surface roughness to prevent scattering losses. 6CCVD provides industry-leading polishing services for SCD, achieving surface roughness of Ra < 1 nm.
- Metalization for Microwave Circuits: The experiment requires the application of microwave fields ($\Omega_{0}, \Omega_{1}$). 6CCVDâs in-house metalization capabilities (Au, Pt, Ti, W, Cu) allow researchers to pattern and deposit high-frequency transmission lines directly onto diamond substrates for efficient delivery of microwave power to the NV center.
- Custom Dimensions and Shapes: If the magnetic field gradient generation requires non-standard component geometries (e.g., specific substrates for magnetic tips or integrated optical components), 6CCVD provides precision laser cutting and etching services for plates/wafers up to 125mm (PCD).
Engineering Support
Section titled âEngineering Supportâ6CCVDâs in-house team of PhD material scientists and technical engineers can assist researchers in material selection and optimization for complex quantum systems.
- We provide expert consultation to optimize SCD growth parameters (e.g., nitrogen incorporation, crystal orientation) to maximize NV center yield and coherence time for similar Quantum State Engineering and Optomechanics projects.
- We offer technical guidance on selecting optimal metalization stacks and processes necessary for integrating low-loss microwave control circuitry required for dressed-state coherence.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Nonclassical states of macroscopic objects are promising for ultrasensitive\nmetrology as well as testing quantum mechanics. In this work, we investigate\ndissipative mechanical quantum state engineering in an optically levitated\nnanodiamond. First, we study single-mode mechanical squeezed states by\nmagnetically coupling the mechanical motion to a dressed three-level system\nprovided by a Nitrogen-vacancy center in the nanoparticle. Quantum coherence\nbetween the dressed levels is created via microwave fields to induce a\ntwo-phonon transition, which results in mechanical squeezing. Remarkably, we\nfind that in ultrahigh vacuum quantum squeezing is achievable at room\ntemperature with feedback cooling. For moderate vacuum, quantum squeezing is\npossible with cryogenic temperature. Second, we present a setup for two\nmechanical modes coupled to the dressed three levels, which results in two-mode\nsqueezing analogous to the mechanism of the single-mode case. In contrast to\nprevious works, our study provides a deterministic method for engineering\nmacroscopic squeezed states without the requirement for a cavity.\n