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Register a new userQuantum phases transition revealed by the exceptional point in Hopfield-Bogoliubov matrix
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We use the exceptional point in Hopfield-Bogoliubov matrix to find the phase transition points in the bosonic system. In many previous jobs, the excitation energy vanished at the critical point. It can be stated equivalently that quantum critical point is obtained when the determinant of Hopfield-Bogoliubov matrix vanishes. We analytically obtain the Hopfield-Bogoliubov matrix corresponding to the general quadratic Hamiltonian. For single-mode system the appearance of the exceptional point in Hopfield-Bogoliubov matrix is equivalent to the disappearance of the determinant of Hopfield-Bogoliubov matrix. However, in multi-mode bosonic system, they are not equivalent except in some special cases. For example, in the case of perfect symmetry, that is, swapping any two subsystems and keeping the total Hamiltonian invariable, the exceptional point and the degenerate point coincide all the time when the phase transition occurs. When the exceptional point and the degenerate point do not coincide, we find a significant result. With the increase of two-photon driving intensity, the normal phase changes to the superradiant phase, then the superradiant phase changes to the normal phase, and finally the normal phase changes to the superradiant phase.
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Recent advances in non-Hermitian physical systems have led to numerous novel optical phenomena and applications. However, most realizations are limited to classical systems and quantum fluctuations of light is unexplored. For the first time, we report the observation of quantum correlations between light channels in an anti-symmetric optical system made of flying atoms. Two distant optical channels coupled dissipatively, display gain, phase sensitivity and quantum correlations with each other, even under linear atom-light interaction within each channel. We found that quantum correlations emerge in the phase unbroken regime and disappears after crossing the exceptional point. Our microscopic model considering quantum noise evolution produces results in good qualitative agreement with experimental observations. This work opens up a new direction of experimental quantum nonlinear optics using non-Hermitian systems, and demonstrates the viability of nonlinear coupling with linear systems by using atomic motion as feedback.
Distinct from closed quantum systems, non-Hermitian system can have exceptional points (EPs) where both eigenvalues and eigenvectors coalesce. Recently, it has been proposed and demonstrated that EPs can enhance the performance of sensors in terms of amplification of detected signal. Meanwhile, the noise might also be amplified at EPs and it is not obvious whether exceptional points will still improve the performance of sensors when both signal and noise are amplified. We develop quantum noise theory to systematically calculate the signal and noise associated with the EP sensors. We then compute quantum Fisher information to extract a lower bound of the sensitivity of EP sensors. Finally, we explicitly construct an EP sensing scheme based on heterodyne detection to achieve the same scaling of the ultimate sensitivity with enhanced performance. Our results can be generalized to higher order EPs for any bosonic non-Hermitian system with linear interactions.
We study the quantum evolution of a non-Hermitian qubit realized as a sub-manifold of a dissipative superconducting transmon circuit. Real-time tuning of the system parameters results in non-reciprocal quantum state transfer associated with proximity to the exceptional points of the effective Floquet Hamiltonian. We observe chiral geometric phases accumulated under state transport, verifying the quantum coherent nature of the evolution in the complex energy landscape and distinguishing between coherent and incoherent effects associated with exceptional point encircling. Our work demonstrates an entirely new method for control over quantum state vectors, highlighting new facets of quantum bath engineering enabled through time-periodic (Floquet) non-Hermitian control.
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.
We present a formal geometric framework for the study of adiabatic quantum mechanics for arbitrary finite-dimensional non-degenerate Hamiltonians. This framework generalizes earlier holonomy interpretations of the geometric phase to non-cyclic states appearing for non-Hermitian Hamiltonians. We start with an investigation of the space of non-degenerate operators on a finite-dimensional state space. We then show how the energy bands of a Hamiltonian family form a covering space. Likewise, we show that the eigenrays form a bundle, a generalization of a principal bundle, which admits a natural connection yielding the (generalized) geometric phase. This bundle provides in addition a natural generalization of the quantum geometric tensor and derived tensors, and we show how it can incorporate the non-geometric dynamical phase as well. We finish by demonstrating how the bundle can be recast as a principal bundle, so that both the geometric phases and the permutations of eigenstates can be expressed simultaneously by means of standard holonomy theory.
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