Observation of parity-time symmetry breaking in a single spin system (1812.05226v1)

Abstract: A fundamental axiom of quantum mechanics requires the Hamiltonians to be Hermitian which guarantees real eigen-energies and probability conservation. However, a class of non-Hermitian Hamiltonians with Parity-Time ($\mathcal{PT}$) symmetry can still display entirely real spectra. The Hermiticity requirement may be replaced by $\mathcal{PT}$ symmetry to develop an alternative formulation of quantum mechanics. A series of experiments have been carried out with classical systems including optics, electronics, microwaves, mechanics and acoustics. However, there are few experiments to investigate $\mathcal{PT}$ symmetric physics in quantum systems.Here we report the first observation of the $\mathcal{PT}$ symmetry breaking in a single spin system. We have developed a novel method to dilate a general $\mathcal{PT}$ symmetric Hamiltonian into a Hermitian one, which can be realized in a practical quantum system.Then the state evolutions under $\mathcal{PT}$ symmetric Hamiltonians, which range from $\mathcal{PT}$ symmetric unbroken to broken regions, have been experimentally observed with a single nitrogen-vacancy (NV) center in diamond. Due to the universality of the dilation method, our result opens a door for further exploiting and understanding the physical properties of $\mathcal{PT}$ symmetric Hamiltonian in quantum systems.

• The paper demonstrates the first experimental observation of PT symmetry breaking in a single spin system using a novel Hermitian dilation method.
• It employs a nitrogen-vacancy center in diamond with precise microwave and RF control to emulate non-Hermitian dynamics across different symmetry regimes.
• The results reveal periodic oscillations in the unbroken phase and decaying dynamics in the broken phase, validating key theoretical predictions.

Observational Study on Parity-Time Symmetry Breaking in a Single Spin System

The paper "Observation of parity-time symmetry breaking in a single spin system" presents a significant experimental paper focused on observing parity-time ($\mathcal{PT}$) symmetry breaking within a quantum system, specifically using a single nitrogen-vacancy (NV) center in diamond. The authors propose a novel strategy for dilating a general $\mathcal{PT}$-symmetric Hamiltonian into a Hermitian one, which allows them to explore the dynamical evolution of quantum states governed by such Hamiltonians in the unbroken and broken symmetry regions.

Key Concepts and Methodology

The central theme of this work revolves around the nature of non-Hermitian Hamiltonians exhibiting $\mathcal{PT}$ symmetry. While quantum mechanics traditionally hinges on the Hermiticity of Hamiltonians to ensure real eigenvalues, non-Hermitian systems with $\mathcal{PT}$ symmetry can also possess entirely real spectra, thereby offering an opportunity to expand our understanding of quantum phenomena.

To paper these systems experimentally in quantum domains, a viable approach is required to emulate $\mathcal{PT}$-symmetric dynamics using available quantum mechanical systems. The authors employ a dilation method where a $\mathcal{PT}$-symmetric Hamiltonian is expressed as a Hermitian Hamiltonian in an enlarged Hilbert space by introducing an ancillary system (ancilla qubit). This method is notable for its universality, being applicable to arbitrary-dimensional, $\mathcal{PT}$-symmetric Hamiltonians.

Experimental Realization

The experimental platform utilized is the NV center in diamond, which serves as a controllable quantum system with well-defined electron and nuclear spin states. Through precise microwave and radio-frequency pulses, the researchers induced the evolution described by the dilated Hermitian Hamiltonian. They explored the state dynamics by examining the population of the NV center's spin states with varying parameters $r$, which dictate the system's proximity to, or membership within, $\mathcal{PT}$ unbroken, broken, or exceptional point regimes.

Results Overview

The reported experimental results demonstrate distinctive behaviors in the quantum state evolution depending on the value of $r$. Notably:

• In the $\mathcal{PT}$ unbroken region ($|r| < 1$), state evolution exhibited periodic oscillations, indicative of real eigenenergies.
• At the exceptional point ($|r| = 1$), the dynamical evolution corresponded to coalescing eigenvalues.
• In the $\mathcal{PT}$ broken regime ($|r| > 1$), state evolutions were marked by decaying behaviors pointing to complex eigenvalues emergence.

These observations substantiate the presence of a $\mathcal{PT}$ symmetry transition and effectively corroborate the theoretical predictions surrounding the energy eigenstructure dependent on parameter $r$.

Theoretical and Practical Implications

The findings from this paper underscore the practicability of simulating non-Hermitian quantum mechanics within existing quantum platforms by leveraging Hermitian dilation methods. Practically, they touch upon the advantage of broadened control over quantum state dynamics using NV centers and other similar quantum systems. Theoretically, such experimental verification opens pathways for deeper investigations into non-Hermitian physics and possible utilization in quantum computation, sensing, and beyond. Furthermore, with this method's universality, a wide array of $\mathcal{PT}$-symmetry-related phenomena become investigable, fueling potential advancements in applications like single-mode lasers and unidirectional transport systems.

Future Prospects

This work calls for further research on various complex non-Hermitian quantum systems, as the dilation method offers a systematic approach to exploring broader aspects of $\mathcal{PT}$ symmetry breaking and related quantum field theories. Possible expansions in experimental designs to increase system complexity or incorporate additional quantum degrees of freedom are potential areas for future exploration.

In conclusion, the reported first observation of $\mathcal{PT}$ symmetry breaking in single spin systems marks a significant step in non-Hermitian quantum mechanics, providing theoretical insights and practical directions for future quantum information science advancements.