Adiabaticity Criterion Research Articles

Study of the adiabatic passage in tripod atomic systems in terms of the Riemannian geometry of the Bloch sphere

We present an analysis of the stimulated Raman adiabatic passage (STIRAP) processes based on the methods of differential geometry. The present work was inspired by an excellent article by Shore et al (Unanyan et al 1999 Phys. Rev. A 59 2910). We demonstrate how a purely geometric interpretation of the adiabatic passage in quantum tripod systems as a Riemannian parallel transport of the dark state vector along the Bloch sphere allows describing the evolution of the system for a given sequence of Stokes, pump and control laser excitation pulses. In combination with the Dykhne–Davis–Pechukas adiabaticity criterion and the minimax principle for circles on a sphere, this approach allows obtaining the analytical form of the optimal laser pulse sequences for a high fidelity tripod fractional STIRAP. In contrast to the conventional STIRAP in Λ-systems, the Gaussian approximations of the optimal laser pulse sequences allow reaching the infidelity of 10−7 for the adiabaticity parameter of 300 without noticeable oscillatory or other detrimental effects on population transfer accuracy.

Adiabatic theorem revisited: The unexpectedly good performance of adiabatic passage

Adiabatic passage employs a slowly varying time-dependent Hamiltonian to control the evolution of a quantum system along the Hamiltonian eigenstates. For processes of finite duration, the exact time evolving state may deviate from the adiabatic eigenstate at intermediate times, but in numerous applications it is observed that this deviation reaches a maximum and then decreases significantly towards the end of the process. We provide a straightforward theoretical explanation for this welcome but often unappreciated fact. Our analysis emphasizes a separate adiabaticity criterion for high fidelity state-to-state transfer and it points to new effective shortcut strategies for near adiabatic dynamics.

Engineering Adiabaticity for Efficient Design of Photonic Lanterns

We present a comprehensive systematic framework for optimizing adiabaticity in photonic lanterns. The framework considers the effects of both the cross-sectional and longitudinal device parameters on adiabaticity. Photonic lanterns are adiabatic photonic devices and are therefore known to have large device lengths. A Shortcuts-to-adiabaticity (STA) protocol is employed to optimize the adiabatic taper profile in all-fibre photonic lanterns. The method tailors adiabatic propagation of light in the system by appropriately correcting the local slope of the taper profile. A quantifiable measure of adiabaticity is established, based on the adiabaticity criterion. This measure relates inversely to the device length and is a useful parameter in taper optimization. We apply the protocol to reported photonic lantern devices to obtain optimal adiabatic taper profiles having shorter device lengths. The optimized taper profile refers to that taper profile which corresponds to the minimum local inter-modal coupling at every point along the quasi-adiabatic transition for a given device length. While optimizing the adiabatic transition by minimizing inter-modal coupling is the basic aim of this work, length optimization is an extremely useful by-product. This procedure can be used to either reduce the device length or to reduce the mode-coupling losses or both. This study analyses reported three and six-core mode selective photonic lanterns as examples. We also discuss ways to make the optimum profiles practically realizable.

Weak Guidance, Multi-index and Exact Mode Eigenvalue Calculation for Mode Intensity Profiles in Tapers

The fundamental mode intensity profile is calculated for different points along the transition of an optical fibre taper from standard size (125 μm external cladding diameter and 8 μm core diameter) down to micro (1 μm external fibre diameter) and submicro size (down to 440 nm fibre diameter) at 1550 nm operational wavelength. The first section of the taper was evaluated using weak guidance approximation, the second section was treated as a three-index layer structure (double-clad) and evaluated with eigenvalue equations for three refractive indices. An external medium being a liquid with a refractive index close to silica is being considered. The third and thinnest section of the taper was evaluated with the exact mode eigenvalue equation. The results show that the fundamental mode intensity for the third section show a discontinuity just at the fibre edge with a peak amplitude larger than the optical field at the centre of the fibre. The taper shape that complies with the adiabaticity criterion and how the mode intensity profile and the spot size (Petermann 1 definition) of the fundamental mode change along their position on the taper were determined.

Fundamental mode intensity evolution in tapered optical fibres

The mode field intensity, spot size, central peak intensity evolution and adiabaticity are calculated for different points along the transition of an optical fibre taper that adiabatically tapers from the standard 125 nm down to 1 µm and then to 440 nm diameter for low loss operation at 1550 nm wavelength. The first section of the taper is evaluated using a weak guidance approximation. The second section is treated as a three-index layer structure (double-clad) and evaluated with eigenvalue equations for three refractive indices. The third and thinnest section of the taper is studied using an exact mode eigenvalue equation. The results show that the fundamental mode for the third section has a discontinuity at the fibre edge with a peak intensity larger than the intensity at the centre of the fibre. Since the guiding by the core disappears in the first section of the taper, the mode field does not simply reduce monotonously along the taper with the outer diameter of the fibre. By this novel approach, and for the first time, to the best of our knowledge, the taper shape that complies with the adiabaticity criterion, the mode intensity profile and the spot size (first Petermann definition) of the fundamental mode evolution, along their position on the taper are determined.

Study on the adiabaticity criterion of the thermally-guided very-large-mode-area fiber.

The adiabaticity criterion of the thermally-guided very-large-mode-area (TG VLMA) fiber is presented based on the mode-coupling theory firstly, to the best of our knowledge. The requirement for the adiabatic propagation of fundamental mode is discussed systematically. It is revealed that the pump absorption plays the most important role and the adiabaticity criterion can be met as long as it is small enough. Then, the effects of the configuration parameters of TG VLMA fiber on the up-limitation of pump absorption for the adiabaticity criterion are investigated. It is found that for the straight TG VLMA fiber, reducing the initial refraction index and inner-cladding diameter and utilizing the bi-directional pumping scheme are beneficial to the adiabatic propagation of fundamental mode. The bent TG VLMA fiber is also studied. It is found that the bent fiber is much more difficult to meet the adiabaticity criterion than the straight one. The results show that even with the 100-cm bend radius, the pump absorption should be smaller than 1 dB/m to meet the adiabaticity criterion. It is suggested that enlarging the core-to-cladding ratio can be helpful for loosening the adiabaticity criterion of bent TG VLMA fiber. These pertinent results can provide significant guidance for understanding and designing the TG VLMA fiber and pertinent lasers and amplifiers.

Comment on "Proton transport in barium stannate: classical, semi-classical and quantum regimes" by G. Geneste, A. Ottochian, J. Hermet and G. Dezanneau, Phys. Chem. Chem. Phys., 2015, 17, 19104.

In a recent paper in this journal, proton transport in oxides was considered in terms of density functional theory and the non-adiabatic Flynn-Stoneham approach of small polaron type proposed much earlier for metals. Also, regimes of hydrogen diffusion relevant to oxides were reviewed, but the straightforwardly observable channel of low-temperature over-barrier jumps has passed unnoticed. We offer this latter possibility, together with some additional arguments, to make our objection more compelling. There are two major contentious findings in the article. First, in discussing the phonon-assisted quantum regime and the adiabatic coincidence configuration in barium stannate, the article claimed that the models based on a fully non-adiabatic picture for metals cannot be generalized to proton-conducting oxides. It is difficult to agree with such a viewpoint because such generalizations are being published. By means of a counterexample, this comment illustrates the real efficacy of using Flynn-Stoneham-like models in studying these oxides. Second, we have strong grounds for supposing that the main claim of the paper being commented on about the adiabatic nature of the proton transfer is in conflict with general interpretation of small polaron hopping. The exact knowledge of energy barriers for proton transfer is needed to confirm the validity of assuming an adiabatic regime. Since the most likely influence of the functional on the adiabaticity criterion formulation is certainly evident, comparison of the results of Geneste et al. to results obtained with higher functionals may check the validity of the present GGA-PBE scheme.

Quantum non-Abelian hydrodynamics: Anyonic or spin–orbital entangled liquids, nonunitarity of scattering matrix and charge fractionalization

In this article, we develop an exact (nonadiabatic, nonperturbative) density matrix scattering theory for a two component quantum liquid which interacts or scatters off from a generic spin-dependent quantum potential. The generic spin dependent quantum potential [Eq. (1)] is a matrix potential, hence, adiabaticity criterion is ill-defined. Therefore the full matrix potential should be treated nonadiabatically. We succeed in doing so using the notion of vectorial matrices which allows us to obtain an exact analytical expression for the scattered density matrix (SDM), ϱsc[Eq. (30)]. We find that the number or charge density in scattered fluid, Tr (ϱsc), expressions in Eqs. (32) depends on nontrivial quantum interference coefficients, [Formula: see text], which arises due to quantum interference between spin-independent and spin-dependent scattering amplitudes and among spin-dependent scattering amplitudes. Further it is shown that Tr (ϱsc) can be expressed in a compact form [Eq. (39)] where the effect of quantum interference coefficients can be included using a vector Qαβ, which allows us to define a vector order parameterQ. Since the number density is obtained using an exact scattered density matrix, therefore, we do not need to prove that Q is non-zero. However, for sake of completeness, we make detailed mathematical analysis for the conditions under which the vector order parameterQ would be zero or nonzero.We find that in presence of spin-dependent interaction the vector order parameterQ is necessarily nonzero and is related to the commutator and anti-commutator of scattering matrix S with its dagger S†[Eq. (78)]. It is further shown that Q≠0, implies four physically equivalent conditions,i.e., spin-orbital entanglement is nonzero, non-Abelian scattering phase, i.e., matrices, scattering matrix is nonunitary and the broken time reversal symmetry for SDM. This also implies that quasi particle excitation are anyonic in nature, hence, charge fractionalization is a natural consequence. This aspect has also been discussed from the perspective of number or charge density conservation, which implies i.e., Tr (ϱ}sc) = Tr (ϱin). On the other hand Q = 0 turns out to be a mathematically forced unphysical solution in presence of spin-dependent potential or scattering which is equivalent to Abelian hydrodynamics, unitary scattering matrix, absence of spin-space entanglement and preserved time reversal symmetry. We have formulated the theory using mesoscopic language, specifically, we have considered two terminal systems connected to spin-dependent scattering region, which is equivalent to having two potential wells separated by a generic spin-dependent potential barrier. The formulation using mesoscopic language is practically useful because it leads directly to the measured quantities such as conductance and spin-polarization density in the leads, however, the presented formulation is not limited to the mesoscopic system only, its generality has been stressed at various places in this article.

Adiabaticity condition for non-Hermitian Hamiltonians

We generalize the concept of population for non-Hermitian systems in different ways and identify the one best suited to characterize adiabaticity. An approximate adiabaticity criterion consistent with this choice is also worked out. Examples are provided for different processes involving two-level atoms with decay.

Robust two-dimensional subrecoil Raman cooling by adiabatic transfer in a tripod atomic system

We demonstrate two-dimensional robust Raman cooling in a four-level tripod system, in which velocity selective population transfer is achieved by a stimulated Raman adiabatic passage. In contrast to basic two-dimensional Raman cooling with square-envelope pulses [Phys. Rev. A 83, 023407 (2011)], the technique presented here allows for a wide variation in the pulse duration and amplitude once the adiabaticity criterion is satisfied. An efficient population transfer together with attainment of a narrow spread of the resonant-velocity group leads to the narrowing of the velocity-distribution spread down to $0.1{v}_{\mathrm{rec}}$, corresponding to an effective temperature equal to $0.01{T}_{\mathrm{rec}}$. This robust method opens additional possibilities for cooling of neutral atoms.

Adiabaticity criterion and the shortest adiabatic mode transformer in a coupled-waveguide system

By analyzing the propagating behavior of the supermodes in a coupled-waveguide system, we have derived a universal criterion for designing adiabatic mode transformers. The criterion relates epsilon, the fraction of power scattered into the unwanted mode, to waveguide design parameters and gives the shortest possible length of an adiabatic mode transformer, which is approximately 2/piepsilon1/2 times the distance of maximal power transfer between the waveguides. The results from numerical calculations based on a transfer-matrix formalism support this theory very well.

Measurement scheme of the Berry phase in superconducting circuits

We present a measurement scheme for observing the Berry phase in a flux assisted Cooper pair pump - the Cooper pair sluice. In contrast to the recent experiments, in which the sluice was employed to generate accurate current through a resistance, we consider a device in a superconducting loop. This arrangement introduces a connection between the pumped current and the Berry phase accumulated during the adiabatic pumping cycles. From the adiabaticity criterion, we derive equations for the maximum pumped current and optimize the sluice accordingly. These results apply also to the high accuracy pumping which results in a potential candidate for a metrological current standard. For measuring the pumped current, an additional Josephson junction is installed into the superconducting loop. We show in detail that the switching of this system from superconducting state into normal state as a consequence of an external current pulse through it may be employed to probe the pumped current. The experimental realization of our scheme would be the first observation of the Berry phase in superconducting circuits.

Aspects of Aqueous Iron and Manganese (II/III) Self-Exchange Electron Transfer Reactions

Ab initio methods were applied to the calculation of the reorganization energy λ and the electronic coupling matrix element VAB for the outer-sphere Fe(OH2)6II/III and Mn(OH2)6II/III self-exchange electron transfer (ET) reactions. For the Fe case, we find an appreciable effect on VAB depending on whether the minority spin electron occupies the dxy orbital or a mixture of dxz/dyz orbitals in the FeII ion. While these two possible nearly isoenergetic electron accepting states alter the magnitude and distance dependence of VAB, they do not affect the internal reorganization energy λI to any significant level. The magnitude and distance dependence of VAB are found to be strongly dependent on encounter orientation, as expected. VAB values for corner-to-corner encounter orientations are substantially larger at any given ET distance considered than those for face-to-face encounter orientations. Values of the decay parameter β are in good agreement with well-accepted values. The adiabaticity criterion is tied to orientation and distance dependence of VAB.

IMPLICATION OF BARRIER FLUCTUATIONS ON THE RATE OF WEAKLY ADIABATIC ELECTRON TRANSFER

The problem of escape of a Brownian particle in a cusp-shaped metastable potential is of special importance in nonadiabatic and weakly-adiabatic rate theory for electron transfer (ET) reactions. For the weakly-adiabatic reactions, the reaction follows an adiabaticity criterion in the presence of a sharp barrier. In contrast to the nonadiabatic case, the ET kinetics can be, however considerably influenced by the medium dynamics. In this paper, the problem of the escape time over a dichotomously fluctuating cusp barrier is discussed with its relevance to the high temperature ET reactions in condensed media.

Slowing down of light by laser induced barrier hopping

We suggest that a very significant reduction in the group velocity of light occurs in a laser induced barrier-hopping process, known as “Laser Catalysis.” In this process a system is made to hop over a potential barrier via a virtual transition to an excited bound state. As in electromagnetically induced transparency (EIT), the light absorption is predicted to dip to zero at a certain frequency, thereby also changing the refractive index, inducing in turn the slowing down of the group velocity of the light. In contrast to EIT, a single pulse is predicted to induce its own transparency and in contrast to self-induced transparency the process is predicted to be insensitive to the pulse area (as long as the pulse is intense enough to meet the adiabaticity criterion). Thus, the medium becomes transparent to the light, as the laser induced barrier-hopping process brings about a fundamental change in the medium.

Ignition delay of non-premixed stagnation-point flows

Ignition delay of stagnation-point oxidizing flows over a wall with the injection of fuel is analyzed numerically. The validity of various criteria of ignition delay, i.e., the adiabaticity criterion and the thermal runaway criteria (∂ 2 T max/∂ t 2=0 and ∂ 2 ω max/∂ t 2=0), is investigated for the problems of cold flow/hot wall and hot flow/cold wall. For cold flow/hot wall systems, the ignition delay decreases with the mass flux of fuel ( m w) if m w is below a critical value ( m w,c). The ignition delay is kinetically controlled for m w< m w,c. For m w> m w,c, the ignition delay increases with m w and is diffusionally controlled by the deficient oxidizer. The adiabaticity criterion is suggested from the viewpoints of practice and simplicity. For hot flow/cold wall systems, the ignition delay decreases with m w and is diffusionally controlled by the deficient fuel. The criterion of ∂ 2 ω max/∂ t 2=0 is suggested both qualitatively and quantitatively. In addition, the effects of flow strain rate, Lewis numbers and Prandtl number on ignition delay are investigated.

Bose-Einstein Condensates in Optical Lattices

We study an ultracold dilute gas of bosonic atoms in an optical lattice induced by intersecting laser beams. As a first approximation we neglect confining potential and atom-atom interactions. In this case the Gross-Pitaevskij equation reduces to simple Mathieu equation. Upon choosing periodic boundary conditions this problem has well known periodic solution. This simple picture allows to demonstrate localization of the wave packet and formation of the band structure. We calculate spectrum of the excited states as a function of the strength of modulating potential and using a standard adiabaticity criterion we predict the most efficient way to ramp up optical lattice, without higher state excitation. Finally, we discuss the influence of the atom-atom interaction (nonlinearity) on the adiabaticity of the process.

Spatial evolution of short laser pulses under coherent population trapping

Spatial and temporal evolution is studied of two powerful short laser pulses having different wavelengths and interacting with a dense three-level Lambda-type optical medium under coherent population trapping. A general case of unequal oscillator strengths of the transitions is considered. Durations of the probe pulse and the coupling pulse $T_{1,2}$ ($T_2>T_1$) are assumed to be shorter than any of the relevant atomic relaxation times. We propose analytical and numerical solutions of a self-consistent set of coupled Schr\"{o}dinger equations and reduced wave equations in the adiabatic limit with the account of the first non-adiabatic correction. The adiabaticity criterion is also discussed with the account of the pulse propagation. The dynamics of propagation is found to be strongly dependent on the ratio of the transition oscillator strengths. It is shown that envelopes of the pulses slightly change throughout the medium length at the initial stage of propagation. This distance can be large compared to the one-photon resonant absorption length. Eventually, the probe pulse is completely reemitted into the coupling pulse during propagation. The effect of localization of the atomic coherence has been observed similar to the one predicted by Fleischhauer and Lukin (PRL, {\bf 84}, 5094 (2000).

Nonlinear Oscillations in One-Zone Stellar Model*The project supported by National Natural Science Foundation of China

If one-zone models are available for some pulsating stars and the motion remains close to adiabaticity, the oscillation and stability criterion of the star have been analyzed by canonical perturbation theory and optimal control theory, separately under different function values on the right-hand side of Eq. (10). We found that (i) If the introduction of a given perturbation function of time b(t) is substituted into the right-hand side of Eq. (10), and energy-optimal control of a nonlinear oscillator is satisfied, the oscillation in one-zone model is unstable. (ii) If is subject to the constraint , and time-optimal control is satisfied, the oscillation in one-zone stellar model is stable. (iii) The periodic oscillation criterion is obtained by a simple method, if b is regarded as a constant of integration in Eq. (10). It shows that the adiabatic exponent is all important. When is greater than or equal to 4/3, the periodic oscillation should occur in one-zone stellar model; when is less than 4/3, and under the additional condition of , the periodic oscillation could not occur in this model.

Thermoelastic stress analysis under nonadiabatic conditions

Thermoelastic stress analysis is a full-field stress measurement technique complementary to local techniques like strain gages. Generally, the heat transfer inside the material is neglected with respect to the frequency of the cyclical loading. An adiabaticity criterion is established to assert this simplification as a function of the thermal diffusion length and the spatial stress gradients. Under nonadiabatic conditions, heat diffusion attenuates the spatial temperature gradients, which leads to an underestimation of stress concentrations. Analytical and numerical considerations allow for the quantification of the spatial resolution. Finally, several inverse techniques can restore the thermally attenuated contrasts.