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Magnetically Induced Two-Phonon Blockade in a Hybrid Spin–Mechanical System

MetadataDetails
Publication Date2024-05-31
JournalMagnetochemistry
AuthorsHongyue Liu, Tai-Shuang Yin, Aixi Chen
InstitutionsZhejiang Sci-Tech University
Citations1
AnalysisFull AI Review Included

This research proposes and theoretically demonstrates a method for achieving a two-phonon blockade in a hybrid spin-mechanical system, extending the concept of quantum blockade from single to multiphonon states.

  • Core Achievement: Implementation of a two-phonon blockade effect, characterized by simultaneous two-phonon bunching (g(2)(0)ss > 1) and three-phonon antibunching (g(3)(0)ss < 1).
  • System Architecture: A hybrid system consisting of a Nitrogen-Vacancy (NV) center spin qubit strongly coupled to a nanomechanical resonator.
  • Mechanism: The coupling is mediated by a strong second-order magnetic gradient, which induces a two-phonon nonlinear interaction (Jaynes-Cummings type).
  • Key Finding: The two-phonon blockade is achieved only when the NV spin qubit is weakly driven under two-phonon resonance (Ω = 2ωm). Weakly driving the mechanical resonator, conversely, only yields a single-phonon blockade.
  • Practical Constraints: The effect is highly sensitive to thermal noise (requiring nth to be minimized) and qubit dephasing (requiring weak γz).
  • Significance: Provides a pathway for engineering multiphonon quantum coherent devices and advancing quantum phononics.

The following specifications relate to the theoretical model and the required operational parameters for achieving the two-phonon blockade effect.

ParameterValueUnitContext
NV Center Spin StateS = 1 tripletN/AElectronic ground state
Zero-Field Splitting (D)~2.88GHzCharacteristic NV center splitting
Coupling TypeQuadratic (g(b + b)2Sz)N/ASecond-order magnetic gradient induced
Strong Coupling Ratio (g/γm)10N/ANormalized coupling strength used in simulations
Qubit Driving Strength (εdm)0.06 to 0.73N/ARequired range for stable two-phonon blockade
Resonance ConditionΩ = 2ωmN/AEffective qubit transition frequency equals twice the mechanical frequency
Thermal Noise Requirementnth < 10-3N/ANonclassical phonon property is destroyed above this level
Two-Phonon Blockade Metricg(2)(0)ss > 1N/ARequired for two-phonon bunching
Three-Phonon Antibunching Metricg(3)(0)ss < 1N/ARequired for three-phonon antibunching

The study utilizes a theoretical model based on quantum optics principles applied to a hybrid solid-state system, solved via the master equation formalism.

  1. System Setup: Modeling of a single NV center spin positioned on top of a mechanical oscillator, with coupling achieved by symmetrically positioning two cylindrical nanomagnets to generate a second-order magnetic gradient (G = d2B/dz2(0)).
  2. Hamiltonian Derivation: The system Hamiltonian (H) includes the NV spin, the mechanical oscillator (Hm = ωmbb), and the second-order magnetic gradient coupling (g(b + b)2Sz).
  3. Effective Two-Level System: The NV spin is treated as an effective two-level system (qubit) under specific driving conditions (εx << {ωx, D, ωx - D}).
  4. Two-Phonon Jaynes-Cummings Model: Applying the rotating-wave approximation (RWA) under the two-phonon resonant condition (Ω = 2ωm) yields the effective Hamiltonian (Heff), which is a coherently driven two-phonon Jaynes-Cummings model.
  5. Dissipative Dynamics: The system dynamics are governed by the Master Equation, incorporating mechanical decay (γm), thermal phonon occupation (nth), and qubit dephasing (γz).
  6. Phonon Statistics Characterization: The steady-state quantum behavior is quantified by numerically calculating the equal-time second-order (g(2)(0)ss) and third-order (g(3)(0)ss) correlation functions.

This research contributes foundational knowledge critical for the development of next-generation quantum technologies, particularly those leveraging mechanical degrees of freedom.

  • Quantum Information Processing (QIP): The ability to control and block specific numbers of phonons is essential for building quantum gates and coherent quantum memories utilizing mechanical resonators.
  • Quantum Phononics: Engineering nonclassical mechanical states and creating tailored phonon sources, such as phonon streams with specific multiphonon bundle emissions.
  • Solid-State Quantum Devices: Utilizing NV centers in diamond—a robust solid-state qubit platform—for scalable hybrid quantum systems that interface spin, mechanical, and potentially photonic modes.
  • Quantum Sensing: The underlying spin-mechanical coupling mechanisms are relevant for developing ultra-sensitive sensors for magnetic fields or mechanical motion, leveraging the high coherence of NV spins.
  • Nanomechanical Resonator Design: Provides design criteria for creating strong nonlinearities in nanomechanical systems using magnetic field gradients, moving beyond traditional optomechanical coupling.
View Original Abstract

Phonon blockade is an important quantum effect for revealing the quantum behaviors of mechanical systems. For a nitrogen-vacancy center spin strongly coupled to a mechanical resonator via the second-order magnetic gradient, we show that the qubit driving can lead to the implementation of the two-phonon blockade, while the usual mechanical driving only allows for the appearance of a single-phonon blockade. As a signature, we investigate three-phonon antibunching with a simultaneous two-phonon bunching process by numerically calculating the second-order and third-order correlation functions. We also analyze in detail the influence of the system parameters (including the qubit driving strength, the dephasing rate of the qubit, as well as the thermal phonon number) on the quality of the two-phonon blockade effect. Our work provides an alternative method for extending the concept of a phonon blockade from a single phonon to multiphonon. It is of direct relevance for the engineering of multiphonon quantum coherent devices and thus has potential applications in quantum information processing.