J. L. Lucio M.
We point out limitations to the analogy between the continuous variable and spin 1/2 systems and show that the maximal violation of Bell inequality is related to an infinite degeneracy. We quantify non-maximal violation of the Bell-CHSH inequality and comment potential experimental implications of our work.
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We study the complex geometric phase acquired by the resonant states of an open quantum system which evolves irreversibly in a slowly time dependent environment. In analogy with the case of bound states, the Berry phase factors of resonant states are holonomy group elements of a complex line bundle with structure group C*. In sharp contrast with bound states, accidental degeneracies of resonances produce a continuous closed line of singularities formally equivalent to a continuous distribution of "magnetic" charge on a "diabolical" circle, in consequence, we find different classes of topologic…
There is a striking convergence between Burgers turbulence and the continuous spontaneous localization [CSL] model of quantum mechanics. In this paper, we exploit this analogy showing the similarities in the physics of these two apparently unrelated problems. It is hoped that the kind of analogy we introduce here may lead to important developments in both areas.
Asymptotic non-Hermitian degeneracy phenomenon and its exactly solvable simulation
本文探讨非厄米特退化现象的渐近性，并构造可解的玩具模型来模拟其特性，揭示EP与IEP奇异性的差异。
Photonic quantum information processing using the frequency continuous-variable of single photons
本文利用频率与正交分量的数学类比，将Hong-Ou-Mandel效应推广至频率域，提出基于频率工程化双光子态的干涉策略以实现随模式数反比缩放的相位精度增强，并推广了高斯玻色子采样模型。
An unconventional method of continuous solid-state cryogenic cooling utilizing the electron subband degeneracy of semiconductor heterostructures is proposed in this Letter. An electrostatic heat pump is modeled, which employs subband "expansion" and "compression" to reach sub-dilution refrigeration temperatures with the fundamental limit set by electron-phonon interaction. Using an ultra-wide GaAs quantum well as an example, the cooling power per unit volume is estimated to reach $4.5\ \rm mW/cm^3$ with a hot-side temperature of $300\ \rm mK$, suitable for applications such as quantum computer…
We develop a geometric construction to prove the inevitability of the electronic ground-state (adiabatic) Berry phase for a class of Jahn-Teller models with maximal continuous symmetries and N > 2 intersecting electronic states. Given that vibronic ground-state degeneracy in JT models may be seen as a consequence of the electronic Berry phase, and that any JT problem may be obtained from the subset we investigate in this letter by symmetry-breaking, our arguments reveal the fundamental origin of the vibronic ground-state degeneracy of JT models.
By analogy to classical cryptography, we develop a "quantum public key" based cryptographic scheme in which the two public and private keys consist in each of two entangled beams of squeezed light. An analog message is encrypted by modulating the phase of the beam sent in public. The knowledge of the degree of non classical correlation between the beam quadratures measured in private and in public allows only the receiver to decrypt the message. Finally, in a view towards absolute security, we formally prove that any external intervention of an eavesdropper makes him vulnerable to any subseque…
We generalize Bell's inequalities to biparty systems with continuous quantum variables. This is achieved by introducing the Bell operator in perfect analogy to the usual spin-1/2 systems. It is then demonstrated that two-mode squeezed vacuum states display quantum nonlocality by using the generalized Bell operator. In particular, the original Einstein-Podolsky-Rosen entangled states, which are the limiting case of the two-mode squeezed vacuum states, can maximally violate Bell's inequality due to Clauser, Horne, Shimony and Holt. The experimental aspect of our scheme and nonlocality of arbitra…
We investigate the quantum entanglement of the three modes associated with the three-photon states obtained by triple-photon generation in a phase-matched third-order nonlinear optical interaction. Although the second order processes have been extensively dealt with, there is no direct analogy between the second and third-order mechanisms. We show for example the absence of quantum entanglement between the quadratures of the three modes in the case of spontaneous parametric triple-photon generation. However, we show that genuine triple-photon entanglement is obtained in the fully seeded case, …
We find an analogy between turbulence and the dynamics of the continuous spontaneous localization model (CSL) of the wave function. The use of a standard white noise in the localization process gives Richardson's t^3 law for the turbulent diffusion, while the introduction of an affine noise in the CSL allows us to obtain the intermittency corrections to this law.
We extensively discuss the Hong-Ou-Mandel experiment taking an original phase-space-based perspective. For this, we analyze time and frequency variables as quantum continuous variables in perfect analogy with position and momentum of massive particles or with the electromagnetic field's quadratures. We discuss how this experiment can be used to directly measure the time-frequency Wigner function and implement logical gates in these variables. We also briefly discuss the quantum/classical aspects of this experiment providing a general expression for intensity correlations that explicit the diff…
For suitable parameters, the classical Duffing oscillator has a known bistability in its stationary states, with low- and high-amplitude branches. As expected from the analogy with a particle in a double-well potential, transitions between these states become possible either at finite temperature, or in the quantum regime due to tunneling. In this analogy, besides local stability, one can also discuss global stability by comparing the two potential minima. For the Duffing oscillator, the stationary states emerge dynamically so that a priori, a potential-minimum criterion for them does not exis…
We prove that a quantum spin chain with half-odd-integral spin cannot have a unique ground state with a gap, provided that the interaction is short ranged, translation invariant, and possesses time-reversal symmetry or ${\mathbb Z}_2 \times {\mathbb Z}_2$ symmetry (i.e., the symmetry with respect to the $π$ rotations of spins about the three orthogonal axes). The proof is based on the deep analogy between the matrix product state formulation and the representation of the Cuntz algebra in the von Neumann algebra $π({\mathcal A}_{R})''$ constructed from the ground state restricted to the right h…
We show by general arguments that networks whose density of states contains few highly degenerate eigenvalues result in inefficient performances of continuous-time quantum walks (CTQW) over these networks, while systems whose eigenvalues all have the same degeneracy lead to very efficient transport. We exemplify our results by considering CTQW and, for comparison, its classical counterpart, continuous-time random walks, over simple structures, whose eigenvalues and eigenstates can be calculated analytically. Extensions to more complicated, hyper-branched networks are discussed.
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