Macroscopic quantum phenomena such as lasers, Bose-Einstein condensates, superfluids, and superconductors are of great importance in foundations and applications of quantum mechanics. In particular, quantum superposition of a large number of spins in
solids is highly desirable for both quantum information processing and ultrasensitive magnetometry. Spin ensembles in solids, however, have rather short collective coherence time (typically less than microseconds). Here we demonstrate that under realistic conditions it is possible to maintain macroscopic quantum superposition of a large spin ensemble (such as about ~10^{14} nitrogen-vacancy center electron spins in diamond) with an extremely long coherence time ~10^8 sec under readily accessible conditions. The scheme, following the mechanism of superradiant lasers, is based on superradiant masing due to coherent coupling between collective spin excitations (magnons) and microwave cavity photons. The coherence time of the macroscopic quantum superposition is the sum of the magnon life time and the cavity lifetime, further elongated by the total number of coherent magnons and photons, which have macroscopic values when masing occurs. The macroscopic quantum coherence of spin ensembles can be exploited for magnetometry with sensitivity ~10 fT/(Hz)^{1/2}. The long-living collective states of spin ensembles in solids will provide a new platform for studying macroscopic quantum phenomena and are useful for quantum technologies.
A quantum object can accumulate a geometric phase when it is driven along a trajectory in a parameterized state space with non-trivial gauge structures. Inherent to quantum evolutions, a system can not only accumulate a quantum phase but may also exp
erience dephasing, or quantum diffusion. Here we show that the diffusion of quantum trajectories can also be of geometric nature as characterized by the imaginary part of the geometric phase. Such an imaginary geometric phase results from the interference of geometric phase dependent fluctuations around the quantum trajectory. As a specific example, we study the quantum trajectories of the optically excited electron-hole pairs, driven by an elliptically polarized terahertz field, in a material with non-zero Berry curvature near the energy band extremes. While the real part of the geometric phase leads to the Faraday rotation of the linearly polarized light that excites the electron-hole pair, the imaginary part manifests itself as the polarization ellipticity of the terahertz sidebands. This discovery of geometric quantum diffusion extends the concept of geometric phases.
Lee-Yang zeros are points on the complex plane of magnetic field where the partition function of a spin system is zero and therefore the free energy diverges. Lee-Yang zeros and their generalizations are ubiquitous in many-body systems and they fully
characterize the analytic properties of the free energy and hence thermodynamics of the systems. Determining the Lee-Yang zeros is not only fundamentally important for conceptual completeness of thermodynamics and statistical physics but also technically useful for studying many-body systems. However, Lee-Yang zeros have never been observed in experiments, due to the intrinsic difficulty that Lee-Yang zeros would occur only at complex values of magnetic field, which are unphysical. Here we report the first observation of Lee-Yang zeros, by measuring quantum coherence of a probe spin coupled to an Ising-type spin bath. As recently proposed, the quantum evolution of the probe spin introduces a complex phase factor, and therefore effectively realizes an imaginary magnetic field on the bath. From the measured Lee-Yang zeros, we reconstructed the free energy of the spin bath and determined its phase transition temperature. This experiment demonstrates quantum coherence probe as a useful approach to studying thermodynamics in the complex plane, which may reveal a broad range of new phenomena that would otherwise be inaccessible if physical parameters are restricted to be real numbers.
Central spin decoherence is useful for detecting many-body physics in environments and moreover, the spin echo control can remove the effects of static thermal fluctuations so that the quantum fluctuations are revealed. The central spin decoherence a
pproach, however, is feasible only in some special configurations and often requires uniform coupling between the central spin and individual spins in the baths, which are very challenging in experiments. Here, by making analogue between central spin decoherence and depolarization of photons, we propose a scheme of Faraday rotation echo spectroscopy (FRES) for studying quantum fluctuations in interacting spin systems. The echo control of the photon polarization is realized by flipping the polarization with a birefringence crystal. The FRES, similar to spin echo in magnetic resonance spectroscopy, can suppress the effects of the static magnetic fluctuations and therefore reveal dynamical magnetic fluctuations. We apply the scheme to a rare-earth compound LiHoF4 and calculate the echo signal, which is related to the quantum fluctuations of the system. We observe enhanced signals at the phase boundary. The FRES should be useful for studying quantum fluctuations in a broad range of spin systems, including cold atoms, quantum dots, solid-state impurities, and transparent magnetic materials.
Quantum evolution of particles under strong fields can be essentially captured by a small number of quantum trajectories that satisfy the stationary phase condition in the Dirac-Feynmann path integrals. The quantum trajectories are the key concept to
understand extreme nonlinear optical phenomena, such as high-order harmonic generation (HHG), above-threshold ionization (ATI), and high-order terahertz sideband generation (HSG). While HHG and ATI have been mostly studied in atoms and molecules, the HSG in semiconductors can have interesting effects due to possible nontrivial vacuum states of band materials. We find that in a semiconductor with non-vanishing Berry curvature in its energy bands, the cyclic quantum trajectories of an electron-hole pair under a strong terahertz field can accumulate Berry phases. Taking monolayer MoS$_2$ as a model system, we show that the Berry phases appear as the Faraday rotation angles of the pulse emission from the material under short-pulse excitation. This finding reveals an interesting transport effect in the extreme nonlinear optics regime.
We show that the correlations in stochastic outputs of time-distributed weak measurements can be used to study the dynamics of an individual quantum object, with a proof-of-principle setup based on small Faraday rotation caused by a single spin in a
quantum dot. In particular, the third order correlation can reveal the true spin decoherence, which would otherwise be concealed by the inhomogeneous broadening effect in the second order correlations. The viability of such approaches lies in that (1) in weak measurement the state collapse which would disturb the system dynamics occurs at a very low probability, and (2) a shot of measurement projecting the quantum object to a known basis state serves as a starter or stopper of the evolution without pumping or coherently controlling the system as otherwise required in conventional spin echo.
In coherent control, electromagnetic vacuum fluctuations usually cause coherence loss through irreversible spontaneous emission. However, since the dissipation via emission is essentially due to correlation of the fluctuations, when emission ends in
a superposition of multiple final states, correlation between different pathways may build up if the which-way information is not fully resolved (i.e., the emission spectrum is broader than the transition energy range). Such correlation can be exploited for spin-flip control in a $Lambda$-type three-level system, which manifests itself as an all-optical spin echo in nonlinear optics with two orders of optical fields saved as compared with stimulated Raman processes. This finding represents a new class of optical nonlinearity induced by electromagnetic vacuum fluctuations.
We propose to create a biexciton by a coherent optical process using a frequency-sweeping (chirped) laser pulse. In contrast to the two-photon Rabi flop scheme, the present method uses the state transfer through avoided level crossing and is a geomet
ric control. The proposed process is robust against pulse area uncertainty, detuning, and dephasing. The speed of the adiabatic operation is constrained by the biexciton binding energy.
