Exceptional Point and Cross-Relaxation Effect in a Hybrid Quantum System
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2021-04-19 |
| Journal | PRX Quantum |
| Authors | Guo-Qiang Zhang, Zhen Chen, Da Xu, Nathan Shammah, Meiyong Liao |
| Institutions | State Key Laboratory of Modern Optical Instruments, Institute of Microelectronics |
| Citations | 67 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”This research reports the experimental realization of an Exceptional Point (EP) in a compact, on-chip hybrid quantum system, leveraging the unique properties of nitrogen defects in diamond.
- Exceptional Point (EP) Demonstration: An EP was observed in a hybrid system consisting of dense P1 centers (nitrogen defects) in Type-1b diamond coupled to a superconducting coplanar-waveguide (CPW) resonator operating at 20 mK.
- Precise Coupling Control: The magnon-photon coupling strength (geff) was precisely tuned over a wide range by applying a microwave drive tone, enabling the system to reach the EP condition (2geff = γ - κ).
- Robustness and Cross-Relaxation Proof: The EP observation remained robust and symmetric regardless of which of the three P1 spin subensembles (s=0, s=+, or s=-) was pumped. This robustness convincingly proves the existence and effectiveness of the cross-relaxation mechanism in equalizing magnon occupations across the subensembles.
- Compact Architecture: The on-chip CPW design provides a highly compact configuration, significantly reducing the system size compared to traditional three-dimensional microwave cavity magnonics setups.
- Platform for Non-Hermitian Physics: This system offers a tunable platform for exploring advanced non-Hermitian phenomena, including enhanced quantum sensing and dynamic encircling of EPs.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Operating Temperature | 20 | mK | Dilution refrigerator environment. |
| Resonator Material | Niobium (50 nm thick) | Film | Fabricated on thermally oxidized silicon substrate. |
| Resonator Central Conductor Width | 20 | µm | Coplanar waveguide geometry. |
| Resonator Gap to Ground Plane | 11.6 | µm | Coplanar waveguide geometry. |
| Resonator Characteristic Impedance | 50 | Ω | Standard impedance matching. |
| Bare Resonator Frequency (ωc/2π) | 3.093 | GHz | Tuned to be resonant with s=0 magnons. |
| Resonator Decay Rate (κ/2π) | 0.6 ± 0.05 | MHz | Extracted from polariton line width. |
| P1 Center Gyromagnetic Ratio (γe/2π) | 28 | GHz/T | Fundamental property of P1 centers. |
| P1 Center Hyperfine Interaction (A||/2π) | 94 | MHz | Defines frequency splitting between subensembles. |
| s=0 Magnon Damping Rate (γ/2π) | 11.9 ± 0.3 | MHz | Half width at half maximum (HWHM). |
| Effective Coupling Strength (geff/2π) | 17.2 ± 0.5 | MHz | Extracted from Rabi splitting (no drive). |
| Exceptional Point (EP) Drive Power (Pd) | -93.7 | dBm | Power required to achieve EP for s=0 pump. |
| Probe Power (Weak) | -120 | dBm | Corresponds to average photon number n = 404. |
| Static Magnetic Field (B) Axis | [100] | Crystal Axis | Applied along the [100] axis of the diamond. |
Key Methodologies
Section titled “Key Methodologies”The experiment utilized a compact, on-chip setup to control and measure the interaction between P1 center magnons and CPW photons under varying drive conditions.
- Device Fabrication and Assembly: A superconducting coplanar-waveguide (CPW) resonator was fabricated using 50-nm-thick niobium film on a silicon substrate. A Type-1b diamond sample containing P1 centers was glued directly onto the resonator.
- Cryogenic Operation and Field Alignment: The device was cooled to 20 mK in a dilution refrigerator. A static magnetic field (B) was applied along the diamond’s [100] axis, tuning the magnon frequencies (ωs) of the three P1 subensembles (s=0, s=±).
- Resonance Condition: The static magnetic field was precisely adjusted to bring the magnons of the s=0 subensemble into resonance with the bare resonator mode (ω0 ≈ ωc ≈ 3.093 GHz).
- Magnon Pumping (Drive Tone): A high-power microwave drive tone (Pd) was applied, resonant with a specific spin subensemble (e.g., s=0, s=+, or s=-), to excite magnons and dynamically tune the effective magnon-photon coupling (geff).
- Steady-State Guarantee: The drive tone was applied for a long duration (3000 s) before each measurement to ensure the system reached a stationary state, allowing cross-relaxation effects to fully manifest.
- Transmission Spectroscopy: A weak, fast probe signal (Pprobe = -120 dBm) was used to measure the transmission spectrum (S21) via a vector-network analyzer (VNA) while sweeping the drive power (Pd).
- EP Identification: The Exceptional Point was identified by observing the coalescence of the two magnon polariton peaks in the transmission spectrum, which occurs when the effective coupling satisfies 2geff = γ - κ.
Commercial Applications
Section titled “Commercial Applications”The demonstrated hybrid quantum system and control methodology have direct relevance to several emerging quantum technologies and high-precision sensing applications.
- Quantum Computing and Information Storage: The system provides a platform for hybrid quantum circuits, utilizing the long coherence times of spin ensembles (P1 centers) coupled strongly to superconducting resonators for quantum memory and processing applications.
- Enhanced Quantum Sensing (Metrology): The ability to operate near an Exceptional Point significantly enhances the sensitivity of the system to tiny perturbations (e.g., shifts in spin frequency or magnetic fields), making it ideal for high-precision magnetometry and metrology protocols.
- On-Chip Microwave Devices: The compact, integrated CPW resonator design facilitates the development of scalable, on-chip quantum devices, moving away from bulky 3D cavity systems.
- Solid-State Masers: The confirmed cross-relaxation effect in P1 centers is the fundamental mechanism used to achieve population inversion, which is essential for developing continuous-wave, room-temperature solid-state masers (microwave amplifiers).
- Non-Reciprocal Devices: The ability to dynamically control the EP allows for future exploration of non-Hermitian phenomena like nonreciprocal energy transfer and asymmetric mode switching, critical for building quantum isolators and circulators.
View Original Abstract
Exceptional points (EPs) are exotic degeneracies of non-Hermitian systems, where the eigenvalues and the corresponding eigenvectors simultaneously coalesce in parameter space, and these degeneracies are sensitive to tiny perturbations on the system. Here, we report an experimental observation of the EP in a hybrid quantum system consisting of dense nitrogen (P1) centers in diamond coupled to a coplanar-waveguide resonator. These P1 centers can be divided into three subensembles of spins and cross relaxation occurs among them. As a new method to demonstrate this EP, we pump a given spin subensemble with a drive field to tune the magnon-photon coupling in a wide range. We observe the EP in the middle spin subensemble coupled to the resonator mode, irrespective of which spin subensemble is actually driven. This robustness of the EP against pumping reveals the key role of the cross relaxation in P1 centers. It offers a novel way to convincingly prove the existence of the cross-relaxation effect via the EP.