Symmetric Double-well Potential Research Articles

Influence of atomic mass centre moving on spontaneous emission in double-well potential

The interaction between a two-level atom trapped in symmetric double-well potential and a single mode cavity field is investigated. By solving Schrödinger equation, the analytical expressions of the total wave function and inversion of the atomic energy level for the whole system are given. Time evolution of the atomic population inversion is analyzed for different initial states of the cavity field, such as fock and coherent states. Influence of atomic mass centre motion on population inversion is considered. Results show that by choosing appropriate cavity field initial state, potential well location and related factors, the spontaneous emission rate of an atom can be effectively controlled and the atomic moving centre of mass can suppress Rabi oscillation.

Observation of the Ring-Puckering Vibrational Mode in Thietane Cation

We have measured the high-resolution vibrational spectra of a thietane (trimethylene sulfide) cation in the gas phase by employing the vacuum ultraviolet mass-analyzed threshold ionization (VUV-MATI) spectroscopic technique. Peaks in the low-frequency region of the observed MATI spectrum of thietane originate from a progression of the ring-puckering vibrational mode (typical in small heterocyclic molecules), which is successfully reproduced by quantum-chemical calculations with 1D symmetric double-well potentials along the ring puckering coordinates on both the S0 and D0 states, the ground electronic states of neutral and cation of thietane, respectively. The values of the interconversion barrier and the ring-puckering angle on the S0 state, the parameters used for the quantum-chemical calculations, were assumed to be 274 cm-1 and 26°. The barrier and the angle on the D0 state, however, are found to be 48.0 cm-1 and 18.2°, respectively, where such small barrier height and puckering angle for the cation suggest that the conformation of thietane cation on the D0 state should be more planar than that of the thietane neutral.

Erasure without Work in an Asymmetric Double-Well Potential.

According to Landauer's principle, erasing a memory requires an average work of at least kTln2 per bit. Recent experiments have confirmed this prediction for a one-bit memory represented by a symmetric double-well potential. Here, we present an experimental study of erasure for a memory encoded in an asymmetric double-well potential. Using a feedback trap, we find that the average work to erase can be less than kTln2. Surprisingly, erasure protocols that differ subtly give measurably different values for the asymptotic work, a result we explain by showing that one protocol is symmetric with the respect to time reversal, while the other is not. The differences between the protocols help clarify the distinctions between thermodynamic and logical reversibility.

Quantum Phase Transitions with Parity-Symmetry Breaking and Hysteresis.

Symmetry-breaking quantum phase transitions play a key role in several condensed matter, cosmology and nuclear physics theoretical models1-3. Its observation in real systems is often hampered by finite temperatures and limited control of the system parameters. In this work we report for the first time the experimental observation of the full quantum phase diagram across a transition where the spatial parity symmetry is broken. Our system is made of an ultra-cold gas with tunable attractive interactions trapped in a spatially symmetric double-well potential. At a critical value of the interaction strength, we observe a continuous quantum phase transition where the gas spontaneously localizes in one well or the other, thus breaking the underlying symmetry of the system. Furthermore, we show the robustness of the asymmetric state against controlled energy mismatch between the two wells. This is the result of hysteresis associated with an additional discontinuous quantum phase transition that we fully characterize. Our results pave the way to the study of quantum critical phenomena at finite temperature4, the investigation of macroscopic quantum tunneling of the order parameter in the hysteretic regime and the production of strongly quantum entangled states at critical points5.

Interface Dynamics of a Metastable Mass-Conserving Spatially Extended Diffusion

We study the metastable dynamics of a discretised version of the mass-conserving stochastic Allen-Cahn equation. Consider a periodic one-dimensional lattice with $N$ sites, and attach to each site a real-valued variable, which can be interpreted as a spin, as the concentration of one type of metal in an alloy, or as a particle density. Each of these variables is subjected to a local force deriving from a symmetric double-well potential, to a weak ferromagnetic coupling with its nearest neighbours, and to independent white noise. In addition, the dynamics is constrained to have constant total magnetisation or mass. Using tools from the theory of metastable diffusion processes, we show that the long-term dynamics of this system is similar to a Kawasaki-type exchange dynamics, and determine explicit expressions for its transition probabilities. This allows us to describe the system in terms of the dynamics of its interfaces, and to compute an Eyring-Kramers formula for its spectral gap. In particular, we obtain that the spectral gap scales like the inverse system size squared.

Coupled spin-vortex pair in dipolar spinor Bose-Einstein condensates

We investigate the ground-state and magnetic properties of a dipolar spin-1 Bose-Einstein condensate trapped in a symmetric double-well potential. In particular, we focus on the spin-vortex states by assuming that each potential well is highly pancake shaped. We show that the presence of the double-well potential gives rise to two different spin configurations for the spin-vortex pair states. We also study the response of the coupled spin-vortex pair to static transverse magnetic fields.

The convective viscous Cahn–Hilliard equation: Exact solutions

In this paper, we give exact solutions for the convective viscous Cahn--Hilliard equation. This equation with a general symmetric double-well potential and Burgers-type convective term was introduced by T. P. Witelski (1996 Studies in Applied Mathematics96, 277–300) to study the joint effects of nonlinear convection and viscosity. We consider this equation with a polynomial, generally asymmetric potential. We also consider both Burgers-type and cubic convective terms. We obtained exact travelling-wave solutions for both cases. For the former case, with an additional constraint on nonlinearity and viscosity, we also obtained an exact two-wave solution.

Transition state theory approach to polymer escape from a one dimensional potential well.

The rate of escape of an ideal bead-spring polymer in a symmetric double-well potential is calculated using transition state theory (TST) and the results compared with direct dynamical simulations. The minimum energy path of the transitions becomes flat and the dynamics diffusive for long polymers making the Kramers-Langer estimate poor. However, TST with dynamical corrections based on short time trajectories started at the transition state gives rate constant estimates that agree within a factor of two with the molecular dynamics simulations over a wide range of bead coupling constants and polymer lengths. The computational effort required by the TST approach does not depend on the escape rate and is much smaller than that required by molecular dynamics simulations.

Detection of small single-cycle signals by stochastic resonance using a bistable superconducting quantum interference device

We propose and experimentally demonstrate detecting small single-cycle and few-cycle signals by using the symmetric double-well potential of a radio frequency superconducting quantum interference device (rf-SQUID). We show that the response of this bistable system to single- and few-cycle signals has a non-monotonic dependence on the noise strength. The response, measured by the probability of transition from initial potential well to the opposite one, becomes maximum when the noise-induced transition rate between the two stable states of the rf-SQUID is comparable to the signal frequency. Comparison to numerical simulations shows that the phenomenon is a manifestation of stochastic resonance.

Applications of the amplitude-phase method to symmetric double-well potentials

An amplitude-phase method is used to derive general quantization conditions for energy levels in smooth double-well potentials. The resulting quantization condition is applied to symmetric double-well potentials, where the two types of symmetry levels are shown to be determined by separate quantization conditions.

Self-trapping and Josephson tunneling solutions to the nonlinear Schrödinger / Gross-Pitaevskii equation

We study the long-time behavior of solutions to the nonlinear Schrodinger / Gross-Pitaevskii equation (NLS/GP) with a symmetric double-well potential. NLS/GP governs nearly-monochromatic guided optical beams in weakly coupled waveguides with both linear and nonlinear (Kerr) refractive indices and zero absorption, as well as the behavior of Bose-Einstein condensates. For small $L^2$ norm (low power), the solution executes beating oscillations between the two wells. There is a power threshold at which a symmetry breaking bifurcation occurs. The set of guided mode solutions splits into two families of solutions. One type of solution is concentrated in either well of the potential, but not both. Solutions in the second family undergo tunneling oscillations between the two wells. A finite dimensional reduction (system of ODEs) derived in [17] is expected to well-approximate the PDE dynamics on long time scales. In particular, we revisit this reduction, find a class of exact solutions and shadow them in the (NLS/GP) system by applying the approach of [17].

Adiabatic tunneling of Bose—Einstein condensates with modulated atom interaction in a double-well potential

We study the adiabatic tunneling of Bose—Einstein condensates in a symmetric double-well potential when the interaction strength between the atoms is modulated linearly or in a cosine periodic form. It is shown that the system evolves along a nonlinear eigenstate path. In the case of linear modulation under the adiabatic approximation conditions, the tunneling probability of the condensate atoms to the other potential well is half. However, when the system is periodically scanned in the adiabatic process, we find an interesting phenomenon. A small change in the cycle period can lead to the condensate atoms returning to the right well or tunneling to the left well. The system comes from a linear eigenstate back to a nonlinear one, which is completely different from the linear eigenstate evolution. We explain the results by using the energy level and the phase diagram.

Tunneling, self-trapping, and manipulation of higher modes of a Bose-Einstein condensate in a double well

We consider an atomic Bose-Einstein condensate trapped in a symmetric one-dimensional double-well potential in the four-mode approximation and show that the semiclassical dynamics of the two ground-state modes can be strongly influenced by a macroscopic occupation of the two excited modes. In particular, the addition of the two excited modes already unveils features related to the effect of dissipation on the condensate. In general, we find a rich dynamics that includes Rabi oscillations, a mixed Josephson-Rabi regime, self-trapping, chaotic behavior, and the existence of fixed points. We investigate how the dynamics of the atoms in the excited modes can be manipulated by controlling the atomic populations of the ground states.

Large amplitude oscillations of protons in water clusters

Synchronous oscillations of bridge protons in molecular rings of (H2O) n water clusters with n = 4–6, 8, and 12 are analyzed as large amplitude motions that result in the inversion of the hydrogen bond sequence in a single ring. The corresponding one-dimensional cross sections of the potential energy surfaces (symmetric double-well potentials) are constructed at the MP2/6–31++G(d, p) level. The eigenstates of the systems in the constructed potentials in the energy range up to the top of the barrier are determined. The synchronous oscillations of protons are shown to be coupled to vibrations of the oxygen skeleton of the molecular ring, and the typical frequencies of the complex vibrations lie in the range of 230–330 cm−1.

Evaluation correlation function of the harmonics oscillator gaussian-cosine rational symmetric double-well potential via numerical shooting method

Evaluation correlation function of the harmonics oscillator gaussian-cosine rational symmetric double-well potential via numerical shooting method

Integrability ofPT-symmetric dimers

The coupled discrete linear and Kerr nonlinear Schr\"odinger equations with gain and loss describing transport on dimers with parity-time ($\mathcal{PT}$)-symmetric potentials are considered. The model is relevant among others to experiments in optical couplers and proposals on Bose-Einstein condensates in $\mathcal{PT}$-symmetric double-well potentials. It is known that the models are integrable. Here, the integrability is exploited further to construct the phase portraits of the system. A pendulum equation with a linear potential and a constant force for the phase difference between the fields is obtained, which explains the presence of unbounded solutions above a critical threshold parameter. The behavior of all solutions of the system, including changes in the topological structure of the phase plane, is then discussed.

Phase transition of Bose—Einstein condensate under decoherence

The effect of decoherence on the phase transition of a Bose—Einstein condensate in a symmetric double-well potential is determined by the mean atom number difference. It still has two phases, the tunneling phase and the self-trapping phase, even under decoherence. The density matrix and the operator fidelity also show very different behaviors in the two phases. This suggests that operator fidelity can be used to characterize the phase transition of this Bose—Einstein condensate model, even under decoherence.

Condensation of Fermions in the double-well potential

The density distribution of ultracold two-component fermionic gases 6Li, which are confined in a gradient magnetic field and a symmetrical double-well potential, is investigated by employing local-density approximation. It is found that three different regimes including quasi-molecular Bose—Einstein condensation (BECm), the dimers in the unitarity limit (ULd), and Bardeen—Cooper—Schrieffer superfluid (BCS) can coexist at the same time. Furthermore, the ranges of these regimes can be controlled to some extent by tuning the gradient of the magnetic field and the parameters characterizing the properties of the double-well potential. This study is of guidance and significance for experimentally realizing the coexistence of BECm, ULd, and BCS in the double-well potential.

Theoretical Modeling of Deuteration-Induced Shifts of the 0–0 Bands in Absorption Spectra of Selected Aromatic Amines: The Role of the Double-Well Potential

The harmonic approximation fails for inversion of the NH2 group in the ground state of aromatic amines as this vibration is characterized by a symmetric double-well potential with relatively small energy barrier. In such cases, the standard harmonic vibrational analysis is inapplicable: the inversion frequency calculated for the bottom of the potential well is strongly overestimated, while it attains imaginary values for the planar conformation of the molecule. The model calculations are discussed taking explicitly into account the presence of the double-well potential. The study is initially focused on reproduction of the deuteration-induced shifts of the 0-0 absorption band for anthranilic acid. The (incorrect) harmonic frequency of the NH2 inversion is replaced by a better one, obtained from numerical calculations employing a simple, quartic-quadratic model for the double-well potential, which is parametrized using just the harmonic frequency of the inversion and the height of the energy barrier. This operation brings theoretical results to qualitative agreement with experiment. A still better match is achieved with a modified version of the model that accounts for mixing of the NH2 inversion mode with other normal modes while retaining the initial simplicity of one-dimensional approach. The corrected results show surprisingly good accuracy, with deviations of the calculated shifts from the experimental values reduced to less than 5 cm(-1). In order to test the performance of the model for systems with higher energy barrier for the NH2 inversion, we have measured the LIF excitation spectra of three different amminobenzonitriles. Partial assignment of the 0-0 bands has been achieved based on their relative intensities for samples with different isotopic exchange ratios. Calculated shifts are in excellent agreement with experimental values for the identified bands. Theoretical predictions are used to complete the assignment of the 0-0 bands in the spectra of the studied amminobenzonitriles.

Eigenvalue structure of a Bose–Einstein condensate in a -symmetric double well

We study a Bose–Einstein condensate in a -symmetric double-well potential where particles are coherently injected in one well and removed from the other well. In mean-field approximation the condensate is described by the Gross–Pitaevskii equation thus falling into the category of nonlinear non-Hermitian quantum systems. After extending the concept of symmetry to such systems, we apply an analytic continuation to the Gross–Pitaevskii equation from complex to bicomplex numbers and show a thorough numerical investigation of the four-dimensional bicomplex eigenvalue spectrum. The continuation introduces additional symmetries to the system which are confirmed by the numerical calculations and furthermore allows us to analyse the bifurcation scenarios and exceptional points of the system. We present a linear matrix model and show the excellent agreement with our numerical results. The matrix model includes both exceptional points found in the double-well potential, namely an EP2 at the tangent bifurcation and an EP3 at the pitchfork bifurcation. When the two bifurcation points coincide the matrix model possesses four degenerate eigenvectors. Close to that point we observe the characteristic features of four interacting modes in both the matrix model and the numerical calculations, which provides clear evidence for the existence of an EP4.