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Entangled microwaves as a resource for entangling spatially separate solid-state qubits - Superconducting qubits, nitrogen-vacancy centers, and magnetic molecules

MetadataDetails
Publication Date2016-06-27
JournalPhysical review. A/Physical review, A
AuthorsAngela Gomez, F. J. RodrĂ­guez, Luis Quiroga, Juan JosĂ© GarcĂ­a‐Ripoll
InstitutionsInstituto de FĂ­sica Fundamental, Universidad de Los Andes
Citations6
AnalysisFull AI Review Included

Entanglement Transfer in Solid-State Qubit Systems via Squeezed Microwaves: A 6CCVD Technical Analysis

Section titled “Entanglement Transfer in Solid-State Qubit Systems via Squeezed Microwaves: A 6CCVD Technical Analysis”

This document analyzes the requirements and findings of the research paper “Entangled microwaves as a resource for entangling spatially separate solid-state qubits: superconducting qubits, NV centers and magnetic molecules” and maps them directly to 6CCVD’s advanced MPCVD diamond capabilities, focusing on material solutions for scalable quantum network engineering.


  • Core Achievement: Demonstration of a robust theoretical protocol for generating steady-state entanglement between two spatially separated solid-state quantum systems (qubits or qubit ensembles) using a continuous, broadband, two-line squeezed microwave field (TLSMF).
  • Key Systems: The protocol is highly relevant for state-of-the-art hybrid systems, specifically Nitrogen Vacancy (NV) centers in diamond, superconducting (SC) qubits, and magnetic molecules.
  • Dissipation Mechanism: Entanglement is transferred via dissipation from the entangled microwave baths, providing a reliable and robust process even in the presence of thermal decoherence.
  • NV Center Feasibility: Experimental parameters appropriate for NV spin ensembles (high density, strong coupling) show that significant entanglement can be achieved with modest microwave squeezing ($s_0 \leq 0.5$, corresponding to a gain of 1.27 dB).
  • Material Requirement: Successful implementation, particularly for NV centers and hybrid SC/NV systems, demands high-quality, low-defect Single Crystal Diamond (SCD) substrates with precise surface preparation and integration capabilities.
  • 6CCVD Value Proposition: 6CCVD provides the necessary high-purity SCD and advanced fabrication services (polishing, metalization, custom dimensions) required to realize and scale these complex quantum architectures.

The following parameters were extracted from the analysis of entanglement generation in solid-state systems coupled to the TLSMF.

ParameterValueUnitContext
NV Center Zero-Field Splitting ($\Delta$)$2 \pi \times 2.87$GHzGround state splitting between $m_s = 0$ and $m_s = \pm 1$ states.
NV Spin Ensemble Coupling ($g$)$2 \pi \times 35$MHzCoupling strength for $N = 3 \times 10^7$ color centers in diamond.
Superconducting Qubit Coupling ($g$)Up to $105$MHzDemonstrated coupling strength in circuit QED experiments.
Required Microwave Squeezing ($s_0$)$\leq 0.5$DimensionlessValue required for appreciable steady-state entanglement in NV ensembles.
Required Squeezing Gain ($G_E$)$1.27$dBCorresponds to $s_0 = 0.5$, calculated as $\cosh^2[s_0]$.
Thermal Decay Rate ($\Gamma^{th}$)$0.7$DimensionlessUsed in simulations to model thermal decoherence effects ($\gamma_{th} = \Gamma^{th} / \Gamma_{1,2}$).
Minimum SCD Polishing RequirementRa < 1nmRequired for high-quality surface integration in hybrid circuit-QED setups.

The theoretical framework relies on advanced quantum optics and condensed matter physics, specifically tailored for open quantum systems.

  1. Entangled Bath Generation: The entangled microwave field (TLSMF) is modeled as a broadband two-line squeezed state, typically generated experimentally using a Josephson Parametric Amplifier (JPA).
  2. Hamiltonian Formulation: The full system Hamiltonian is decomposed into the matter system ($Q_j$), the free microwave field ($R_j$), and the matter-radiation interaction ($V_j$) for two spatially separated branches ($j=1, 2$).
  3. Master Equation Derivation: The dynamics of the reduced density operator $\rho(t)$ are solved using the Liouville-Von Neumann equation, approximated via the Born-Markov and Wigner-Weisskopf approaches, resulting in a Lindblad master equation.
  4. Dissipative Entanglement Transfer: The crucial non-local Lindblad term ($\mathcal{L}_{1,2}$) is responsible for entangling the matter subsystems, driven by the cross-correlations of the squeezed microwave baths.
  5. Decoherence Modeling: Thermal decoherence effects are incorporated by adding a second Lindbladian term ($\mathcal{L}_D$) representing amplitude damping processes associated with thermal excitations (Bose-Einstein occupation number $n$).
  6. Entanglement Quantification: Steady-state entanglement is quantified using the Concurrence ($C^{ss}$) for single qubit pairs and Logarithmic Negativity ($E_N$) for qubit ensembles (Gaussian states).

The successful experimental implementation of this entanglement protocol, particularly involving NV centers in diamond and hybrid circuit-QED architectures, relies heavily on the quality, purity, and customizability of the solid-state material platform. 6CCVD is uniquely positioned to supply the necessary materials and fabrication expertise.

To replicate or extend the research involving NV centers and hybrid quantum circuits, 6CCVD recommends the following materials:

  • Optical Grade Single Crystal Diamond (SCD):

    • Application: Ideal host material for high-coherence NV centers. Required for low-defect density and long spin coherence times, essential for maximizing entanglement duration.
    • Purity: Ultra-high purity SCD is necessary to minimize parasitic decoherence channels not fully accounted for in the thermal model.
    • Thickness: Available in thicknesses from $0.1 \mu$m up to $500 \mu$m, allowing researchers to optimize the diamond layer for specific microwave coupling geometries or integration with bulk substrates.
  • Polycrystalline Diamond (PCD) Substrates:

    • Application: While SCD is preferred for the active NV layer, large-area PCD substrates (up to 125mm) can serve as robust, high-thermal-conductivity carriers for complex, scalable quantum integrated circuits (QICs) operating at cryogenic temperatures.
  • Boron-Doped Diamond (BDD):

    • Application: BDD can be utilized for creating highly conductive diamond layers or electrodes within the QIC, offering an alternative to traditional metal contacts where diamond’s unique thermal and chemical properties are advantageous.

The paper describes coupling solid-state systems directly to transmission lines and resonators, necessitating precise material integration. 6CCVD offers comprehensive customization services critical for circuit-QED integration:

Customization ServiceRelevance to Research Paper6CCVD Capability
High-Precision PolishingEssential for minimizing surface defects and ensuring high-quality interfaces for microwave resonators and metal contacts.SCD: Ra < 1 nm. Inch-size PCD: Ra < 5 nm.
Custom MetalizationRequired for fabricating the superconducting qubits, JPA components, and transmission lines directly onto the diamond surface.In-house deposition of Au, Pt, Pd, Ti, W, and Cu, enabling complex multi-layer stack fabrication.
Custom DimensionsNecessary for scaling the bipartite quantum system (Fig. 1) into larger, multi-qubit quantum networks.Plates/wafers up to 125mm (PCD) and custom-cut SCD pieces.
Substrate ThicknessAllows optimization of microwave coupling and thermal management.Substrates available up to 10mm thickness.

6CCVD’s in-house PhD team specializes in the material science of MPCVD diamond for quantum applications. We can assist researchers with:

  • Material Selection: Optimizing diamond grade (SCD vs. PCD, doping levels) based on specific experimental requirements (e.g., maximizing NV coherence vs. thermal management).
  • Integration Design: Consulting on optimal surface preparation and metalization schemes for hybrid circuit-QED/NV center projects.
  • Scalability Planning: Developing strategies for transitioning from proof-of-concept experiments to scalable, multi-qubit architectures using large-area diamond wafers.

6CCVD provides the foundational diamond materials necessary to advance research in entangled solid-state quantum systems. Our commitment to ultra-high purity, precision fabrication, and global logistics ensures your project receives the highest quality components, delivered globally (DDU default, DDP available).

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Quantum correlations present in a broadband two-line squeezed microwave state\ncan induce entanglement in a spatially separated bipartite system consisting of\neither two single qubits or two qubit ensembles. By using an appropriate master\nequation for a bipartite quantum system in contact with two separate but\nentangled baths, the generating entanglement process in spatially separated\nquantum systems is thoroughly characterized. Our results provide evidence that\nthis entanglement transfer by dissipation is feasible yielding to a\nsteady-state amount of entanglement in the bipartite quantum system which can\nbe optimized for a wide range of realistic physical systems that include\nstate-of-the-art experiments with NV centers in diamond, superconducting qubits\nor even magnetic molecules embedded in a crystalline matrix.\n