Geometric Quantum Phase Research Articles

Uhlmann quench and geometric dynamic quantum phase transition of mixed states

Uhlmann quench and geometric dynamic quantum phase transition of mixed states

Revisiting the missing He–McKellar–Wilkens geometric quantum phase

Revisiting the missing He–McKellar–Wilkens geometric quantum phase

Spin-dependent linear confinement in a magnetic medium

The linear confinement in two-dimensions can yield an analogue of a triangular well or a quantum bouncer. We discuss a way of achieving a linear confinement of a neutral particle with a permanent magnetic dipole moment in a magnetic medium by dealing with a two-dimensional system with cylindrical symmetry. This linear confinement is characterized by being spin-dependent. Then, by including the Aharonov–Casher geometric quantum phase, we show that bound states analogous to those of the quantum bouncer can be achieved, where the energy levels are infinitely degenerated with regard to the ℓ-waves. Further, we obtain the revival time of the system.

Quantum control and Berry phase of electron spins in rotating levitated diamonds in high vacuum

Levitated diamond particles in high vacuum with internal spin qubits have been proposed for exploring macroscopic quantum mechanics, quantum gravity, and precision measurements. The coupling between spins and particle rotation can be utilized to study quantum geometric phase, create gyroscopes and rotational matter-wave interferometers. However, previous efforts in levitated diamonds struggled with vacuum level or spin state readouts. To address these gaps, we fabricate an integrated surface ion trap with multiple stabilization electrodes. This facilitates on-chip levitation and, for the first time, optically detected magnetic resonance measurements of a nanodiamond levitated in high vacuum. The internal temperature of our levitated nanodiamond remains moderate at pressures below 10−5 Torr. We have driven a nanodiamond to rotate up to 20 MHz (1.2 × 109 rpm), surpassing typical nitrogen-vacancy (NV) center electron spin dephasing rates. Using these NV spins, we observe the effect of the Berry phase arising from particle rotation. In addition, we demonstrate quantum control of spins in a rotating nanodiamond. These results mark an important development in interfacing mechanical rotation with spin qubits, expanding our capacity to study quantum phenomena.

Effects of quantum geometric phase of a particle in an oscillating hard-wall spherical trap

Effects of quantum geometric phase of a particle in an oscillating hard-wall spherical trap

Topological effects on generalized Duffin-Kemmer-Petiau oscillator under Aharonov–Bohm flux field and Coulomb potential

In this paper, we study the relativistic quantum motions of the oscillator field of the wave equation under the influence of the Aharonov–Bohm (AB) flux field with a Coulomb vector potential in the background of the topological defects produced by a cosmic string and global monopole space-time. We derive the radial equation of the generalized Duffin-Kemmer-Petiau (DKP) oscillator in a static cosmic string space-time and solve it through the Heun function equation. Afterwards, we derive the radial equation of the same generalized DKP oscillator in a point-like global monopole background and obtain the eigenvalue solutions using the same procedure. The generalized oscillator field is studied by substituting the radial momentum operator ∂ r → (∂ r + i M ω η 0 f(r)), where f(r) is an arbitrary function other than linear and introduces a vector potential of Coulomb-types through a minimal substitution via ∂ μ → (∂ μ − i q A μ ) in the relativistic wave equation. It is shown that the eigenvalue solutions of the oscillator field are influenced by the topological defects of the cosmic string and point-like global monopole space-times and get them modified. Furthermore, we see that the eigenvalue solutions depend on the geometric quantum phase, and hence, shifted them more in addition to the topological defects that show the gravitational analogue to the Aharonov–Bohm effect for the bound-states.

Effects of nontrivial topology with Coulomb-types scalar and vector potential on relativistic quantum motions of scalar charged bosons

In this paper, we study the relativistic quantum motions of spin-zero scalar bosons confined by the quantum flux field in the presence of Coulomb-type scalar potential in the background of a topologically nontrivial 4D space–time. Afterwards, we introduce a Coulomb-like vector potential through a minimal substitution in the wave equation and determine the eigenvalue solutions of the quantum system analytically. In fact, it is shown there that the nontrivial topology of the geometry, Coulomb-types scalar and vector potential, and the quantum flux field influence the energy profile and wave function of the scalar bosons and get them modified. Also, the gravitational analogue of the Aharonov–Bohm effect is observed because the energy eigenvalue depends on the geometric quantum phase.

Thermodynamic Properties and Persistent Currents of Harmonic Oscillator Under AB-Flux Field in a Point-Like Defect with Inverse Square Potential

In this analysis, we study the eigenvalue solution of the non-relativistic particles confined by the Aharonov-Bohm (AB) flux field in the presence of potential the superposition of a harmonic oscillator plus inverse square potential with constant term in the background of a point-like global monopole. Afterwards, we study the thermodynamic properties of the quantum system at finite temperatures $$T\ne 0$$ and calculate the vibrational free energy, mean energy, specific heat capacity, and the entropy by using the partition function $$Z(\beta )$$ . These quantities are then analyzed and show the influences of the topological defect with flux field and potential. We also see that the energy eigenvalue depends on the geometric quantum phase, and thus an electromagnetic analogue of the Aharonov-Bohm effect is observed. This dependence of the eigenvalue gives rise to a persistent current and we analyze the effects of the topological defect with potential on it.

Nonadiabatic heavy atom tunneling in 1nσ*-mediated photodissociation of thioanisole.

The 1nσ*-mediated photodissociation dynamics of thioanisole is investigated quantum mechanically using a three-dimensional model based on a newly constructed diabatic potential energy matrix. The lifetimes of the low-lying S1(1ππ*) resonances are determined and found to accord well with available experimental data. Specifically, our theoretical results demonstrate that the photodissociation of thioanisole at the low-lying S1(1ππ*) levels takes place via the heavy atom tunneling due to the higher S1/S2 conical intersection and two equivalent out-of-plane saddle points appearing on the dissociation path. The isotopic effect on the lifetimes is found to be pronounced, manifesting the nature of the tunneling process. Moreover, the geometric phase effect around the S1/S2 conical intersection is found to slightly impact the lifetimes due to the weak destructive or constructive interferences in this heavy atom tunneling, which differs significantly from the scenario in the nonadiabatic hydrogen atom tunneling. Importantly, the quantum mechanical treatment is essentially required to accurately describe the 1nσ*-mediated photodissociation dynamics of thioanisole owing to involving quantum tunneling and geometric phase effects near the conical intersection.

Topological defects with generalized Hulthen–Coulomb-inverse quadratic Yukawa potential on eigenvalue solution under Aharonov–Bohm flux field

In this work, we solve the radial Schrödinger wave equation in three dimensions under Aharonov–Bohm (AB)-flux field with potential superposition of generalized q-deformed Hulthen potential, Coulomb potential, and inverse quadratic Yukawa potential in a point-like defect. We determine the approximate eigenvalue solution using the parametric Nikiforov–Uvarov (NU) method and analyze the effects of topological defect and the magnetic flux field with this superposed potential. We show an analogous of the AB effect because the eigenvalue solution depends on the geometric quantum phase and bound state solutions are possible under condition. Finally, we utilize the approximate eigenvalue solution to some molecular potential models, such as Deng–Fan potential and inverse quadratic Hulthen potential and analyze the effects on the energy levels and the radial wave functions.

Non-inertial effects on relativistic scalar massive charged bosons in a topologically nontrivial space-time and Aharonov–Bohm effect

In this work, we study the relativistic quantum motions of spin-zero scalar massive charged bosons in a topologically nontrivial four-dimensional rotating space-time in the presence of a uniform magnetic field and quantum flux. Afterwards, a spin-zero relativistic quantum oscillator model is also studied and determines the bound-state eigenvalue solutions of the quantum system. We see that the energy eigenvalue and the wave function get modified by the nontrivial topology of the geometry, the rotating frame of reference, and the magnetic field. We also observed the gravitational analog of the Aharonov–Bohm (AB) effect due to the dependence of the energy eigenvalue on the geometric quantum phase.

Effects of rotating frames of reference and Cornell-type potential on modified quantum oscillator field in magnetic cosmic string space–time

In this paper, a relativistic quantum oscillator model analog to the Dirac oscillator under the effects of a uniform rotating frame of reference in a five-dimensional magnetic cosmic string space–time subject to a Cornell-type scalar potential is analyzed. We discuss the influences of topological defects, the magnetic flux, and the scalar potential on the eigenvalue solution of the wave equation. We see that the presence of uniform rotating frame causes the perturbation of the energy spectrum around [Formula: see text] and observe the Sagnac-type effect. Furthermore, we show that the energy eigenvalue depends on the geometric quantum phase which gives rise to the gravitational analog of the Aharonov–Bohm effect.

Dynamical Casimir effects with atoms: From the emission of photon pairs to geometric phases

The coupling between a moving ground-state atom and the quantum electromagnetic field is at the origin of several intriguing phenomena ranging from the dynamical Casimir emission of photons to Sagnac-like geometric phase shifts in atom interferometers. Recent progress in this emerging field reveals unprecedented connections between non-trivial aspects of modern physics such as electrodynamic retardation, non-unitary evolution in open quantum systems, geometric phases, non-locality and inertia.

Quantum Hall Effect and Geometric Phase Factor in Strong Magnetic Fields

Quantum Hall Effect and Geometric Phase Factor in Strong Magnetic Fields

Missing He–McKellar–Wilkens geometric quantum phase

We discuss the appearance of a missing geometric quantum phase from the interaction of the permanent electric dipole moment of a neutral particle with the magnetic field produced by a uniform distribution of the magnetic charges inside an infinitely long non-conductor cylinder with an inner radius r a . This geometric quantum phase is associated with the missing magnetic charge per unit length in a region with a cylindrical shape of radius r a and gives rise to an analogue of the He–McKellar–Wilkens geometric quantum phase. By searching for bound state solutions, we show that an Aharonov–Bohm-type effect arises from the influence of the missing geometric quantum phase on the eigenvalues of energy.

Geometric quantum phase from the interaction of the permanent electric dipole moment of a neutral particle with an axial magnetic field

Geometric quantum phase from the interaction of the permanent electric dipole moment of a neutral particle with an axial magnetic field

Geometric Phases and The Sagnac Effect: Foundational Aspects and Sensing Applications

AbstractGeometric phase is a key player in many areas of quantum science and technology. In this review article, several foundational aspects of quantum geometric phases and their relations to classical geometric phases are outlined. How the Aharonov–Bohm and Sagnac effects fit into this context is then discussed. Moreover, a concise overview of technological applications of the latter, with special emphasis on gravitational sensing, like in gyroscopes and gravitational wave detectors is presented.

Implementation of Quantum Level Addressability and Geometric Phase Manipulation in Aligned Endohedral Fullerene Qudits.

Endohedral nitrogen fullerenes have been proposed as building blocks for quantum information processing due to their long spin coherence time. However, addressability of the individual electron spin levels in such a multiplet system of 4 S3/2 has never been achieved because of the molecular isotropy and transition degeneracy among the Zeeman levels. Herein, by molecular engineering, we lifted the degeneracy by zero-field splitting effects and made the multiple transitions addressable by a liquid-crystal-assisted method. The endohedral nitrogen fullerene derivatives with rigid addends of spiro structure and large aspect ratios of regioselective bis-addition improve the ordering of the spin ensemble. These samples empower endohedral-fullerene-based qudits, in which the transitions between the 4 electron spin levels were respectively addressed and coherently manipulated. The quantum geometric phase manipulation, which has long been proposed for the advantages in error tolerance and gating speed, was implemented in a pure electron spin system using molecules for the first time.

Implementation of Quantum Level Addressability and Geometric Phase Manipulation in Aligned Endohedral Fullerene Qudits

AbstractEndohedral nitrogen fullerenes have been proposed as building blocks for quantum information processing due to their long spin coherence time. However, addressability of the individual electron spin levels in such a multiplet system of 4S3/2 has never been achieved because of the molecular isotropy and transition degeneracy among the Zeeman levels. Herein, by molecular engineering, we lifted the degeneracy by zero‐field splitting effects and made the multiple transitions addressable by a liquid‐crystal‐assisted method. The endohedral nitrogen fullerene derivatives with rigid addends of spiro structure and large aspect ratios of regioselective bis‐addition improve the ordering of the spin ensemble. These samples empower endohedral‐fullerene‐based qudits, in which the transitions between the 4 electron spin levels were respectively addressed and coherently manipulated. The quantum geometric phase manipulation, which has long been proposed for the advantages in error tolerance and gating speed, was implemented in a pure electron spin system using molecules for the first time.

Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model

We study the quantum metric tensor and its scalar curvature for a particular version of the Lipkin-Meshkov-Glick model. We build the classical Hamiltonian using Bloch coherent states and find its stationary points. They exhibit the presence of a ground state quantum phase transition, where a bifurcation occurs, showing a change of stability associated with an excited state quantum phase transition. Symmetrically, for a sign change in one Hamiltonian parameter, the same phenomenon is observed in the highest energy state. Employing the Holstein-Primakoff approximation, we derive analytic expressions for the quantum metric tensor and compute the scalar and Berry curvatures. We contrast the analytic results with their finite-size counterparts obtained through exact numerical diagonalization and find an excellent agreement between them for large sizes of the system in a wide region of the parameter space, except in points near the phase transition where the Holstein-Primakoff approximation ceases to be valid.