Jian Qi Shen
Three related topics on the quantum-vacuum geometric phases in a noncoplanarly curved optical fiber is presented: (i) a brief review: the investigation of vacuum effect and its experimental realization; (ii) the sequence of ideas of geometric phases in the fiber; (iii) three derivations of effective Hamiltonian that describes the wave propagation of photon field in a curved fiber.
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We study the quantum-vacuum geometric phases resulting from the vacuum fluctuation of photon fields in Tomita-Chiao-Wu noncoplanar curved fibre system, and suggest a scheme to test the potential existence of such vacuum effect. Since the signs of the quantum-vacuum geometric phases of left- and right- handed (LRH) circularly polarized light are just opposite, the total geometric phases at vacuum level is inescapably absent in the fibre experiments performed previously by other authors. By using the present approach where the fibre made of gyroelectric media is employed, the quantum-vacuum geom…
The connection between the quantum-vacuum geometric phases (which originates from the vacuum zero-point electromagnetic fluctuation) and the non-normal product procedure is considered in the present Letter. In order to investigate this physically interesting geometric phases at quantum-vacuum level, we suggest an experimentally feasible scheme to test it by means of a noncoplanarly curved fiber made of gyrotropic media. A remarkable feature of the present experimental realization is that one can easily extract the nonvanishing and nontrivial quantum-vacuum geometric phases of left- and/or righ…
An experimentally feasible realization of testing quantum-vacuum geometric phases of photons by using a gyrotropic-medium optical fibre via Casimir's effect is proposed.
The lateral Casimir-Polder force between an atom and a corrugated surface should allow one to study experimentally non trivial geometrical effects in quantum vacuum. Here, we derive the theoretical expression of this force in a scattering approach that accounts for the optical properties of the corrugated surface. We show that large corrections to the ``proximity force approximation'' could be measured using present-day technology with a Bose-Einstein condensate used as a vacuum field sensor.
We propose a new way to generate an observable geometric phase by means of a completely incoherent phenomenon. We show how to imprint a geometric phase to a system by "adiabatically" manipulating the environment with which it interacts. As a specific scheme we analyse a multilevel atom interacting with a broad-band squeezed vacuum bosonic bath. As the squeezing parameters are smoothly changed in time along a closed loop, the ground state of the system acquires a geometric phase. We propose also a scheme to measure such geometric phase by means of a suitable polarization detection.
In our previous work it has been shown the possibility to use the Aharonov-Anandan invariant as a tool in the analysis of disparate systems, including Hawking and Unruh effects, as well as graphene physics and thermal states. We show that the vacuum condensation, characterizing such systems, is also related with geometric phases and we analyze the properties of the geometric phase of systems represented by mixed state and undergoing a nonunitary evolution. In particular, we consider two level atoms accelerated by an external potential and interacting with a thermal state. We propose the realiz…
The propagation of monomode photons inside a coiled optical fibre was regarded as a time-dependent quantum evolution process, which gives rise to a geometric phase. It is well known that the investigation of non-adiabatic geometric phases ought to be performed only in the Schrödinger picture. So, the projections of photon spin operators onto the fixed frame of reference is discussed in this paper. In addition, we also treat the non-normal-order spin operators and consider the potential effects (e.g., quantum-vacuum geometric phases) of quantum fluctuation fields arising in a curved optical fib…
Spin squeezing by geometric focusing in vacuum Rabi oscillations
该研究提出利用真空拉比振荡的布洛赫球几何聚焦产生自旋压缩，最优压缩参数随原子数变化，压缩对耗散鲁棒，以$^{171}$Yb为例验证方案可行性。
We study the geometric phase acquired by an inertial atom whose trajectories are parallel to a reflecting boundary due its coupling to vacuum fluctuations of electromagnetic fields, by treating the atom as an open quantum system in a bath of the fluctuating vacuum fields, and show that the phase is position dependent as a result of the presence of the boundary which modifies the field quantum fluctuations. Our result therefore suggests a possible way of detecting vacuum fluctuations in experiments involving geometric phase.
We present a new method by which, in principle, it is possible to "see in absolute darkness," i.e., without exchanging any real quanta through quantum fields. This is possible because objects modify the mode structure of the vacuum in their vicinity. The new method probes the mode structure of the vacuum through the Unruh effect, i.e., by recording the excitation rates of quantum systems that are accelerated.
Berry's geometric phase naturally appears when a quantum system is driven by an external field whose parameters are slowly and cyclically changed. A variation in the coupling between the system and the external field can also give rise to a geometric phase, even when the field is in the vacuum state or any other Fock state. Here we demonstrate the appearance of a vacuum-induced Berry phase in an artificial atom, a superconducting transmon, interacting with a single mode of a microwave cavity. As we vary the phase of the interaction, the artificial atom acquires a geometric phase determined by …
A summary of some lines of ideas leading to model-independent frameworks of relativistic quantum field theory is given. It is followed by a discussion of the Reeh-Schlieder theorem and geometric modular action of Tomita-Takesaki modular objects associated with the quantum field vacuum state and certain algebras of observables. The distillability concept, which is significant in specifying useful entanglement in quantum information theory, is discussed within the setting of general relativistic quantum field theory.
We present a bipartite two-level system coupled to electromagnetic quantum vacuum fluctuations through a general dipolar coupling. We derive the master equation in the framework of open quantum systems, assuming an environment composed of (i) solely vacuum fluctuations and (ii) the vacuum fluctuations and a conducting plate located at a fixed distance from the bipartite system. For both cases considered, we study the dynamics of the bipartite system and the temporal evolution of the concurrence of an initial entangled bipartite state. We further analyze the generation of entanglement due to th…
The quantum vacuum contribution to Berry's geometric phase of photon fields inside a noncoplanarly curved (coiled) fiber is considered by means of the second-quantization formulation. It is shown that the quantum vacuum Berry's phases of left- and right-handed circularly polarized light have the equal magnitudes but opposite signs, and are therefore eliminated entirely by each other. In order to realize such a novel vacuum effect, a scheme to separate the quantum vacuum Berry's phase of one polarized light from another by using the chiral medium fiber is suggested. We think the present study m…
We study the geometric curvature and phase of the Rabi model. Under the rotating-wave approximation (RWA), we apply the gauge independent Berry curvature over a surface integral to calculate the Berry phase of the eigenstates for both single and two-qubit systems, which is found to be identical with the system of spin-1/2 particle in a magnetic field. We extend the idea to define a vacuum-induced geometric curvature when the system starts from an initial state with pure vacuum bosonic field. The induced geometric phase is related to the average photon number in a period which is possible to me…
Motivated by the work [Phys. Rev. Lett. 89, 220404 (2002)] for detecting the vacuum-induced Berry phases with two-mode Jaynes-Cummings models (JCMs), we show here that, for a parameter-dependent single-mode JCM, certain atom-field states also acquire the photon-number-dependent Berry phases after the parameter slowly changed and eventually returned to its initial value. This geometric effect related to the field quantization still exists, even the filed is kept in its vacuum state. Specifically, a feasible Ramsey interference experiment with cavity quantum electrodynamics (QED) system is desig…
Quantum Geometric Machine Learning
该论文融合机器学习与微分几何、拓扑，构建开放量子系统数据集，并利用灰盒深度学习、Cartan分解与变分方法解决量子控制及酉综合问题。
In open quantum systems, we study the geometric phases acquired for a two-level atom coupled to a bath of fluctuating vacuum massless scalar fields due to linear acceleration and circular motion without and with a boundary. In free space, as we amplify acceleration, the geometric phase acquired purely due to linear acceleration case firstly is smaller than the circular acceleration case in the ultrarelativistic limit for the initial atomic state $θ\in(0,\fracπ{2})\cup(\fracπ{2},π)$, then equals to the circular acceleration case in a certain acceleration, and finally, is larger than the circula…
We consider an atom (represented by a two-level system) moving in front of a dielectric plate, and study how traces of dissipation and decoherence (both effects induced by vacuum field fluctuations) can be found in the corrections to the unitary geometric phase accumulated by the atom. We consider the particle to follow a classical, macroscopically-fixed trajectory and integrate over the vacuum field and the microscopic degrees of freedom of both the plate and the particle in order to calculate friction effects. We compute analytically and numerically the non-unitary geometric phase for the mo…
The geometric entanglement entropy of a quantum field in the vacuum state is known to be divergent and, when regularized, to scale as the area of the boundary of the region. Here we introduce an operational definition of the entropy of the vacuum restricted to a region: we consider a subalgebra of observables that has support in the region and a finite resolution. We then define the entropy of a state restricted to this subalgebra. For Gaussian states, such as the vacuum of a free scalar field, we discuss how this entropy can be computed. In particular we show that for a spherical region we re…
We report on the quantum electrodynamical analogue of a Sagnac phase induced by the fast rotation of a neutral nanoparticle onto atomic waves propagating in its vicinity. The quantum vacuum Sagnac phase is a geometric Berry phase proportional to the angular velocity of rotation. The persistence of a noninertial effect into the inertial frame is also analogous to the Aharonov-Bohm effect. Here, a rotation confined to a restricted domain of space gives rise to an atomic phase even though the interferometer is at rest with respect to an inertial frame. By taking advantage of a plasmon resonance, …
Two representations of mixed states by state-vectors, known as purified state and thermal vacuum, have been realized on quantum computers. While the two representations look similar, they differ by a partial transposition in the ancilla space. While ordinary observables cannot discern the two representations, we generalize the Berry phase of pure quantum states to mixed states and construct two geometric phases that can reflect the partial transposition. By generalizing the adiabatic condition, we construct the thermal Berry phase, whose values from the two representations can be different, Ho…
Spatially separated bodies in relative motion through vacuum experience a tiny friction force known as quantum friction. This force has so far eluded experimental detection due to its small magnitude and short range. Quantitative details revealing traces of the quantum friction in the degradation of the quantum coherence of a particle are presented. Environmentally induced decoherence for a particle sliding over a dielectric sheet can be decomposed into contributions of different signatures: one solely induced by the electromagnetic vacuum in presence of the dielectric and another induced by m…
Revealing quantum geometry of solids through vacuum fluctuations
本研究通过量子涨落和量子几何力揭示固体中由真空涨落诱导的零点能及其对超导电路的影响。
The presence of noncyclic geometric invariant is revealed in all the phenomena where particle generation from vacuum or vacuum condensates appear. Aharonov--Anandan invariants then can help to study such systems and can represent a new tool to be used in order to provide laboratory evidence of phenomena particulary hard to be detected, such as Hawking and Unruh effects and some features of quantum field theory in curved space simulated by some graphene morphologies. It is finally suggested that a very precise quantum thermometer can be built by exploiting geometric invariants properties.
Disordered geometrical boundaries such as rough surfaces induce important modifications to the mode spectrum of the electromagnetic quantum vacuum. In analogy to Anderson localization of waves induced by a random potential, here we show that the Casimir-Polder interaction between a cold atomic sample and a rough surface also produces localization phenomena. These effects, that represent a macroscopic manifestation of disorder in quantum vacuum, should be observable with Bose-Einstein condensates expanding in proximity of rough surfaces.
Geometry-Induced Vacuum Polarization and Mode Shifts in Maxwell-Klein-Gordon Theory
研究麦克斯韦-克莱因-戈登系统在曲面上的情况，证明几何势充当局部重整化环境，导出长波下相对频率偏移表达式，应用于多种形状识别光谱特征，表明空间曲率可用于“真空工程”提供可测量偏移。
We review a number of ideas related to area law scaling of the geometric entropy from the point of view of condensed matter, quantum field theory and quantum information. An explicit computation in arbitrary dimensions of the geometric entropy of the ground state of a discretized scalar free field theory shows the expected area law result. In this case, area law scaling is a manifestation of a deeper reordering of the vacuum produced by majorization relations. Furthermore, the explicit control on all the eigenvalues of the reduced density matrix allows for a verification of entropy loss along …
Quantum-Geometric Bound on Dynamical Instability in Bosonic Systems
本文针对多模二次玻色系统，推导得到动力学不稳定性最大本征值与Fubini-Study速度的严格量子几何边界，通过共振纯squeezer实现边界饱和，并在失谐参量放大器中验证了边界的不可逆性。
We revisit earlier studies on Berry phases suggested to appear in certain cavity QED settings. It has been especially argued that a non-trivial geometric phase is achievable even in the situation of no cavity photons. We, however, show that such results hinge on imposing the {\it rotating wave approximation} (RWA), while without the RWA no Berry phases occur in these schemes. A geometrical interpretation of our results is obtained by introducing semi-classical energy surfaces which in a simple way brings out the phase space dynamics. With the RWA, a conical intersection between the surfaces em…
The review of vacuum and matter restructuring in space-time with boundaries is presented. We consider phase properties of confining gauge theories and strongly interacting fermion systems. In particular, the chiral and deconfinement phase transitions properties in the presence of Casimir plates. We also discuss mass scale shifts in such systems and their possible dynamical and geometrical nature.
We propose a set of devices of simple geometrical design which may exhibit a permanent rotation due to quantum (vacuum) fluctuations. These objects - which have no moving parts - impose certain boundary conditions on quantum fluctuations thus affecting their vacuum energy similarly to the standard Casimir effect. The boundary conditions are chosen in such a way that the vacuum energy for a static device is larger compared to the energy of the vacuum fluctuations in a state when the device rotates about a certain axis. The optimal frequency of rotation is determined by geometry and moment of in…
We study the Hawking effect in terms of the geometric phase acquired by a two-level atom as a result of coupling to vacuum fluctuations outside a Schwarzschild black hole in a gedanken experiment. We treat the atom in interaction with a bath of fluctuating quantized massless scalar fields as an open quantum system, whose dynamics is governed by a master equation obtained by tracing over the field degrees of freedom. The nonunitary effects of this system are examined by analyzing the geometric phase for the Boulware, Unruh and Hartle-Hawking vacua respectively. We find, for all the three cases,…
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