Travis J. Baker, S. N. Saadatmand, Dominic W. Berry, Howard M. Wiseman
备注：
6 pages, 4 figures, and 31 pages of supplemental information. v2: This paper is now published [Nature Physics DOI:10.1038/s41567-020-01049-3 (26 October 2020)]. For copyright reasons, this arxiv paper is based on a version of the paper prior to the accepted (21 August 2020) version
To quantify quantum optical coherence requires both the particle- and wave-natures of light. For an ideal laser beam [1,2,3], it can be thought of roughly as the number of photons emitted consecutively into the beam with the same phase. This number, $\mathfrak{C}$, can be much larger than $μ$, the number of photons in the laser itself. The limit on $\mathfrak{C}$ for an ideal laser was thought to be of order $μ^2$ [4,5]. Here, assuming nothing about the laser operation, only that it produces a beam with certain properties close to those of an ideal laser beam, and that it does not have external sources of coherence, we derive an upper bound: $\mathfrak{C} = O(μ^4)$. Moreover, using the matrix product states (MPSs) method [6,7,8,9], we find a model that achieves this scaling, and show that it could in principle be realised using circuit quantum electrodynamics (QED) [10]. Thus $\mathfrak{C} = O(μ^2)$ is only a standard quantum limit (SQL); the ultimate quantum limit, or Heisenberg limit, is quadratically better.
The dynamics of coherence in a two-qubit Heisenberg XXX model with magnetic field in the presence of the intrinsic decoherence is investigated. We discuss the influence of dipole parameter, spin distance, magnetic field and initial state parameter on coherence of the long time limit situation. Then, we discuss how decoherence changes with time with the initial state parameter and the decoherence parameter.
Nonlinear Heisenberg-Langevin equations are solved analytically by operator Fourier-expansion for the laser in the LED regime. Fluctuations of populations of lasing levels are taken into account as perturbations. Spectra of operator products are calculated as convolutions, preserving Bose commutations for the lasing field operators. It is found that fluctuations of population significantly affect spontaneous and stimulated emissions into the lasing mode, increase the radiation rate, the number of lasing photons and broad the spectrum of a bad cavity thresholdless and the superradiant lasers. T…
The quantum coherence of the two-site XYZ model with Dzyaloshinsky-Moriya (DM) interactions in an external inhomogenous magnetic field is studied. The DM interaction, the magnetic field and the measurement basis can be along different directions, and we examine the quantum coherence at finite temperature. With respect to the spin-spin interaction parameter, we find that the quantum coherence decreases when the direction of measurement basis is the same as that of the spin-spin interaction. When the spin-lattice interaction is varied, the coherence always increases irrespective of the relation …
Using an ensemble of atoms in an optical cavity, we engineer a family of nonlocal Heisenberg Hamiltonians with continuously tunable anisotropy of the spin-spin couplings. We thus gain access to a rich phase diagram, including a paramagnetic-to-ferromagnetic Ising phase transition that manifests as a diverging magnetic susceptibility at the critical point. The susceptibility displays a symmetry between Ising interactions and XY (spin-exchange) interactions of the opposite sign, which is indicative of the spatially extended atomic system behaving as a single collective spin. Images of the magnet…
We experimentally study the coherence time of a below-threshold Raman laser in which the gain medium is a gas of magneto-optically trapped atoms. The second-order optical coherence exhibits photon bunching with a correlation time which is varied by two orders of magnitude by controlling the gain. Results are in good agreement with a simple analytic model which suggests the effect is dominated by gain, rather than dispersion, in this system. Cavity ring-down measurements show the photon lifetime, related to the first-order coherence time, is also increased.
An uncertainty relation for the Rényi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(α)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any estimate of a random optical phase shift in terms of average photon number, where $f(α)$ is maximised for non-Shannon entropies. Related simple yet strong uncertainty relations linking phase uncertainty to the photon number distribution, such as $ΔΦ\geq \max_n p_n$, are also obtained. These results are significantly strengthened via upper and lower bounds on the Rény…
Combining topologically-protected chiral light transport and laser amplification gives rise to topological lasers, whose operation is immune to fabrication imperfections and defects, uncovering the role of topology in a novel nonlinear non-Hermitian regime. We study a topological laser based on the photonic Haldane model with selective pumping of chiral edge modes described by saturable gain. We investigate elementary excitations around the mean-field steady state and their consequences for the coherence properties. In particular, we show that the hybridization of chiral edge modes gives rise …
The effect of non-uniform magnetic fields on the Ising-Heisenberg chain of a heterotrimetallic coordination compound $\mathrm{Fe-Mn-Cu}$, modeling a magnetic impurity on one dimer is studied. This impurity is configured by imposing non-uniform magnetic fields on each sites of $j-$th interstitial ionic dimer $\mathrm{Mn}^{2+}-\mathrm{Cu}^{2+}$ of the chain model. The quantum coherence and pairwise entanglement between spin-1/2 magnetic $\mathrm{Mn}^{2+}-\mathrm{Cu}^{2+}$ ion dimers clearly depend on the site which the impurity is located. It is demonstrated that when the magnetic impurity is co…
We derive the Heisenberg representation of the ultrafast inverse Faraday effect that provides the time evolution of magnetic vectors of a magnetic system during its interaction with a laser pulse. We obtain a time-dependent effective magnetic operator acting in the Hilbert space of the total angular momentum that describes a process of nonthermal excitation of magnetic precessions in an electronic system by a circularly polarized laser pulse. The magnetic operator separates the effect of the laser pulse on the magnetic system from other magnetic interactions. The effective magnetic operator pr…
We investigate theoretically the quantum-coherence properties of the cathodoluminescence (CL) emission produced by a temporally modulated electron beam. Specifically, we consider the quantum-optical correlations of CL from electrons that are previously shaped by a laser field. The main prediction here is the presence of phase correlations between the emitted CL field and the electron-modulating laser, even though the emission intensity and spectral profile are independent of the electron state. In addition, the coherence of the CL field extends to harmonics of the laser frequency. Since electr…
The atomistic resolution recently achieved by ultrafast spectroscopies demands corresponding theoretical advances. Real-time time-dependent density-functional theory (RT-TDDFT) with Ehrenfest dynamics offers an optimal trade-off between accuracy and computational costs to study electronic and vibrational dynamics of laser-excited materials in the sub-picosecond regime. However, this approach is unable to account for thermal effects or zero-point energies which are crucial in the physics involved. Herein, we adopt a quantum-semiclassical method based on RT-TDDFT+Ehrenfest to simulate laser-indu…
Observation of the First-Order Interference Fringes Beyond Coherence Length Employing Commercial Continuous-wave Multi-mode Laser Diode: A Sight of Two-photon Interference
Short wavelength Free-Electron Lasers (FELs) are the newest light sources available to scientists to probe a wide range of phenomena, with chemical, physical and biological applications, using soft and hard X-rays. These sources include the currently most powerful light sources in the world (hard X-ray sources) and are characterised by extremely high powers and high transverse coherence, but the first FELs had reduced longitudinal coherence. Now it is possible to achieve good longitudinal coherence (narrow bandwidth in the frequency domain) and here we discuss and illustrate a range of experim…
Lasers and Bose-Einstein condensates (BECs) exhibit macroscopic quantum coherence in seemingly unrelated ways. Lasers possess a well-defined global phase and are characterized by large fluctuations in the number of photons. In BECs of atoms, instead, the number of particles is conserved and the global phase is undefined. Here, we present a unified framework to simulate lasers and BECs states in gate-based quantum computers, by mapping bosonic particles to qubit excitations. Our approach relies on a scalable circuit that measures the total number of particles without destroying long-range coher…
We investigate the factorization, coherence and asymmetry properties of the 1d Heisenberg spin-1/2 XXZ chain with Dzyaloshinskii-Moriya interaction (DMI) and a transverse magnetic field using quantum information measures. Both longitudinal and transverse DM vectors are considered. Using numerical DMRG, we compute the one-tangle, two-spin concurrence and the Wigner-Yananse-skew information. We show that a longitudinal DMI destroys the factorizability property while a transverse DMI preserves it. We relate the absence of factorizability to the breaking of the $U(1)$ rotation symmetry about the l…
In a Mach-Zenhder interferometer (MZI), the highest precision for a measurement error is given by vacuum fluctuations of quantum mechanics, resulting in a shot noise limit1,2,3,4,5. Because the intensity measurement in an MZI is correlated with the phase difference, the precision measurement (Δn) is coupled with the phase resolution (Δϕ) by the Heisenberg uncertainty principle. Quantum metrology offers a different solution to this precision measurement using nonclassical light such as squeezed light or higher-order entangled-photon pairs, resulting in a smaller Δϕ for the same Δn3,4,5,6,7,8. H…
The Quantum State of an Ideal Propagating Laser Field
给出了理想连续波激光场的量子信息理论描述，并据此重新解释了典型的量子光学实验。特别是，我们表明，相反，最近的索赔[T。鲁道夫和B。C. Sanders，Phys. Rev. Lett. 87，077903（2001）]，常规激光器可用于具有连续变量的量子隐形传态并用于产生连续变量纠缠。不需要光学相干性，但需要相位相干性。我们还指出相干态在激光描述中起着特殊的作用。
