Breakdown Of Adiabaticity Research Articles

Dynamically crossing diabolic points while encircling exceptional curves: A programmable symmetric-asymmetric multimode switch

Nontrivial spectral properties of non-Hermitian systems can lead to intriguing effects with no counterparts in Hermitian systems. For instance, in a two-mode photonic system, by dynamically winding around an exceptional point (EP) a controlled asymmetric-symmetric mode switching can be realized. That is, the system can either end up in one of its eigenstates, regardless of the initial eigenmode, or it can switch between the two states on demand, by simply controlling the winding direction. However, for multimode systems with higher-order EPs or multiple low-order EPs, the situation can be more involved, and the ability to control asymmetric-symmetric mode switching can be impeded, due to the breakdown of adiabaticity. Here we demonstrate that this difficulty can be overcome by winding around exceptional curves by additionally crossing diabolic points. We consider a four-mode {{{{{{{mathcal{PT}}}}}}}}-symmetric bosonic system as a platform for experimental realization of such a multimode switch. Our work provides alternative routes for light manipulations in non-Hermitian photonic setups.

Triggering single-molecule qubit spin dynamics via non-Abelian geometric phase effects.

We illustrate how macroscopic rotations can be utilised to trigger and control a spin dynamics within the ground doublet of both Kramers and non-Kramers-type molecular nanomagnets via the non-Abelian character of the time-evolution operator. For Kramers magnets, we show how this effect can be harnessed to realise single-qubit quantum gates and give the explicit example of a recently reported CoCl2(tu)4 single-molecule magnet (SMM). We demonstrate that gating operations could be performed on this magnet in as fast as 10 ps before the breakdown of adiabaticity, much faster than typical spin-lattice relaxation times. Based on this effect, we also suggest CoCl2(tu)4 as a quantum gyroscope for sensing yaw-axis rotations. For integer spin nanomagnets where non-axial crystal field interactions often lift ground state degeneracy, we show how spin dynamics from the non-Abelian geometric propagator can be recovered using non-adiabatic macroscopic rotations not-necessarily resonant with the tunnel splitting gap. Using the well-known TbPc2 single-ion magnet as a further example, we identify an experimentally plausible non-adiabatic rotation that induces a coherent superposition of tunnelling ground states, tantamount to preparing each member of a TbPc2 ensemble in the maximal angular momentum state |mJ = 6〉. The detection of an ensuing coherent oscillation of the macroscopic magnetisation polarised along the TbPc2 principal magnetic axis after the completed rotation could then proceed via time-resolved magnetisation measurements.

Ultrafast Symmetry-Breaking Charge Separation in a Perylene Bisimide Dimer Enabled by Vibronic Coupling and Breakdown of Adiabaticity.

Perylene bisimides (PBIs) have received great attention in their applicability to optoelectronics. Especially, symmetry-breaking charge separation (SB-CS) in PBIs has been investigated to mimic the efficient light capturing and charge generation in natural light-harvesting systems. However, unlike ultrafast CS dynamics in donor-acceptor heterojunction materials, ultrafast SB-CS in a stacked homodimer has still been challenging due to excimer formation in the absence of rigidifying surroundings such as a special pair in the natural systems. Herein, we present the detailed mechanism of ultrafast photoinduced SB-CS occurring in a 1,7-bis(N-pyrrolidinyl) PBI dimer within a cyclophane. Through narrow-band and broad-band transient absorption spectroscopy, we demonstrate that ultrafast SB-CS in the dimer is enabled by the combination of (1) vibrationally coherent charge-transfer resonance-enhanced excimer formation and (2) breakdown of adiabaticity (formation of SB-CS diabats) in the excimer state via structural and solvent fluctuation. Quantum chemical calculations also underpin that the participation of strong electron-donating substituents in overall vibrational modes plays a crucial role in triggering the ultrafast SB-CS. Therefore, our work provides an alternative route to facilitate ultrafast SB-CS in PBIs and thereby establishes a novel strategy for the design of optoelectronic materials.

Landau-Zener transitions through a pair of higher-order exceptional points

Non-Hermitian quantum systems with explicit time dependence are of ever increasing importance. There are only a handful of models that have been analytically studied in this context. Here, a $\mathcal{PT}$-symmetric non-Hermitian $N$-level Landau-Zener type problem with two exceptional points of $N\mathrm{th}$ order is introduced. The system is Hermitian for asymptotically large times, far away from the exceptional points, and has purely imaginary eigenvalues between the exceptional points. The full Landau-Zener transition probabilities are derived, and found to show a characteristic binomial behavior. In the adiabatic limit the final populations are given by the ratios of binomial coefficients. It is demonstrated how this behavior can be understood on the basis of adiabatic analysis, despite the breakdown of adiabaticity that is often associated with non-Hermitian systems.

Landau-Zener Transition in the Dynamic Transfer of Acoustic Topological States.

Topological notions in physics often emerge from adiabatic evolution of states. It not only leads to fundamental insight of topological protection but also provides an important approach for the study of higher-dimensional topological phases. In this work, we first demonstrate the transfer of topological boundary states (TBSs) across the bulk to the opposite boundary in an acoustic waveguide system. By exploring the finite-size induced minigap between two TBS bands, we unveil the quantitative condition for the breakdown of adiabaticity in the system by demonstrating the Landau-Zener transition with both theory and experiments. Our results not only serve as a foundation of future studies of dynamic state transfer but also inspire applications leveraging nonadiabatic transitions as a new degree of freedom.

Dynamical Signatures of Ground‐State Degeneracy to Discriminate against Andreev Levels in a Majorana Fusion Experiment

AbstractDetection of the fusion rule of Majora na zero‐modes is a near‐term milestone on the road to topological quantum computation. An obstacle is that the non‐deterministic fusion outcome of topological zero‐modes can be mimicked by the merging of non‐topological Andreev levels. To distinguish these two scenarios, the dynamical signatures of the ground‐state degeneracy that is the defining property of non‐Abelian anyons is searched for. By adiabatically traversing parameter space along two different pathways, one can identify ground‐state degeneracies from the breakdown of adiabaticity. It is shown that the approach can discriminate against accidental degeneracies of Andreev levels.

Many-body adiabatic passage: Quantum detours around chaos

We study the many-body dynamics of stimulated Raman adiabatic passage in the presence of on-site interactions. In the classical mean-field limit, explored in Phys. Rev. Lett. {\bf 121}, 250405 (2018), interaction-induced chaos leads to the breakdown of adiabaticity under the quasi-static variation of the parameters, thus producing {\em low} sweep rate boundaries on efficient population transfer. We show that for the corresponding many-body system, alternative quantum pathways from the initial to the target state, open up at even slower sweep rates. These quantum detours avoid the chaotic classical path and hence allow a robust and efficient population transfer.

Adiabatic Passage through Chaos.

We study the process of nonlinear stimulated Raman adiabatic passage within a classical mean-field framework. Depending on the sign of interaction, the breakdown of adiabaticity in the interacting nonintegrable system is not related to bifurcations in the energy landscape, but rather to the emergence of quasistochastic motion that drains the followed quasistationary state. Consequently, faster sweep rate, rather than quasistatic variation of parameters, is better for adiabaticity.

Oscillating potential well in the complex plane and the adiabatic theorem

A quantum particle in a slowly-changing potential well $V(x,t)=V(x-x_0(\epsilon t))$, periodically shaken in time at a slow frequency $\epsilon$, provides an important quantum mechanical system where the adiabatic theorem fails to predict the asymptotic dynamics over time scales longer than $ \sim 1 / \epsilon$. Specifically, we consider a double-well potential $V(x)$ sustaining two bound states spaced in frequency by $\omega_0$ and periodically-shaken in complex plane. Two different spatial displacements $x_0(t)$ are assumed: the real spatial displacement $x_0(\epsilon t)=A \sin (\epsilon t)$, corresponding to ordinary Hermitian shaking, and the complex one $x_0(\epsilon t)=A-A \exp( -i \epsilon t)$, corresponding to non-Hermitian shaking. When the particle is initially prepared in the ground state of the potential well, breakdown of adiabatic evolution is found for both Hermitian and non-Hermitian shaking whenever the oscillation frequency $\epsilon$ is close to an odd-resonance of $\omega_0$. However, a different physical mechanism underlying nonadiabatic transitions is found in the two cases. For the Hermitian shaking, an avoided crossing of quasi-energies is observed at odd resonances and nonadiabatic transitions between the two bound states, resulting in Rabi flopping, can be explained as a multiphoton resonance process. For the complex oscillating potential well, breakdown of adiabaticity arises from the appearance of Floquet exceptional points at exact quasi energy crossing.

Topology of a dissipative spin: Dynamical Chern number, bath-induced nonadiabaticity, and a quantum dynamo effect

We analyze the topological deformations of a spin-1/2 in an effective magnetic field induced by an ohmic quantum dissipative environment at zero temperature. From Bethe Ansatz results and a variational approach, we confirm that the Chern number is preserved in the delocalized phase for $\alpha<1$. We report a divergence of the Berry curvature at the equator when $\alpha_c=1$ that appears at the localization Kosterlitz-Thouless quantum phase transition in this model. Recent experiments in quantum circuits have engineered non-equilibrium protocols in time to access topological properties at equilibrium from the measure of the (quasi-)adiabatic out-of-equilibrium spin expectation values. Applying a numerically exact stochastic Schr\"{o}dinger equation we find that, for a fixed sweep velocity, the bath induces a crossover from (quasi-)adiabatic to non-adiabatic dynamical behavior when the spin bath coupling increases. We also investigate the particular regime $H/\omega_c \ll v/H \ll 1$, where the dynamical Chern number observable built from out-of-equilibrium spin expectation values vanishes at $\alpha=1/2$. In this regime, the mapping to an interacting resonance level model enables us to characterize the evolution of the dynamical Chern number in the vicinity of $\alpha=1/2$. Then, we provide an intuitive physical explanation of the breakdown of adiabaticity in analogy to the Faraday effect in electromagnetism. We demonstrate that the driving of the spin leads to the production of a large number of bosonic excitations in the bath, which in return strongly affect the spin dynamics. Finally, we quantify the spin-bath entanglement and build an analogy with an effective model at thermal equilibrium.

Quantum Control in Qutrit Systems Using Hybrid Rabi-STIRAP Pulses

We introduce and analyze theoretically a procedure that combines slow adiabatic stimulated Raman adiabatic passage (STIRAP) manipulation with short nonadiabatic Rabi pulses to produce any desired three-level state in a qutrit system. In this protocol, the fast pulses create superpositions between the ground state and the first excited state, while the slow pulses transfer an arbitrary population to the second excited state via STIRAP. We demonstrate high-fidelity quantum control of the level populations and phases and we characterize the errors incurred under the breakdown of adiabaticity. In a configuration where an ancillary state is available, we show how to realize a nondemolition monitoring of the relative phases. These methods are general and can be implemented on any experimental platform where a quantum system with at least three accessible energy levels is available. We discuss here in detail experimental implementations in circuit quantum electrodynamics (QED) based on the results obtained with a transmon, where the control of population using the hybrid Rabi-STIRAP sequence has been achieved.

Dynamically encircling an exceptional point for asymmetric mode switching

Physical systems with loss or gain have resonant modes that decay or grow exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, an 'exceptional point' occurs, giving rise to fascinating phenomena that defy our physical intuition. Particularly intriguing behaviour is predicted to appear when an exceptional point is encircled sufficiently slowly, such as a state-flip or the accumulation of a geometric phase. The topological structure of exceptional points has been experimentally explored, but a full dynamical encircling of such a point and the associated breakdown of adiabaticity have remained out of reach of measurement. Here we demonstrate that a dynamical encircling of an exceptional point is analogous to the scattering through a two-mode waveguide with suitably designed boundaries and losses. We present experimental results from a corresponding waveguide structure that steers incoming waves around an exceptional point during the transmission process. In this way, mode transitions are induced that transform this device into a robust and asymmetric switch between different waveguide modes. This work will enable the exploration of exceptional point physics in system control and state transfer schemes at the crossroads between fundamental research and practical applications.

Transition time of nonlinear Landau–Zener model in adiabatic limit

The impact of nonlinear interaction on the loop structure of lower energy level and on the time evolution curve of canonical momentum which corresponds to the lower eigenstate are analyzed respectively. We find that the curve changes from single-valued to multi-valued as nonlinear interaction grows. The fascinating part is that the time range delimited by turning points in the loop of energy level and the period between two inflexion points on the multi-valued part of the evolution curve of canonical momentum are the same. Therefore, we propose a characteristic time in the transition process of nonlinear Landau–Zener model in adiabatic limit. Last, the physical meaning of the transition time as a measure of how much time the system experiences a structural change which directly results in the breakdown of adiabaticity is discussed.

Nonlinear Landau-Zener tunneling in Majorana’s stellar representation

By representing the evolution of a quantum state with the trajectories of the stars on a Bloch sphere, the Majorana’s stellar representation provides an intuitive way to understand quantum motion in a high dimensional projective Hilbert space. In this work we show that the Majorana’s representation offers a very interesting and intuitive way to understand the nonlinear Landau-Zener tunneling. In particular, the breakdown of adiabaticity in this tunneling phenomenon can be understood as some of the stars never reaching the south pole. We also establish a connection between the Majorana stars in the second quantized model and the single star in the mean field model by using the reduced density matrix.

High-Fidelity Rapid Ground-State Loading of an Ultracold Gas into an Optical Lattice

A protocol is proposed for the rapid coherent loading of a Bose-Einstein condensate into the ground state of an optical lattice, without residual excitation associated with the breakdown of adiabaticity. The driving potential required to assist the rapid loading is derived using the fast-forward technique, and generates the ground state in any desired short time. We propose an experimentally feasible loading scheme using a bichromatic lattice potential, which approximates the fast-forward driving potential with high fidelity.

Bose-Einstein condensates in toroidal traps: Instabilities, swallow-tail loops, and self-trapping

We study the stability and dynamics of an ultracold bosonic gas trapped in a toroidal geometry and driven by rotation in the absence of dissipation. We first delineate, via the Bogoliubov mode expansion, the regions of stability and the nature of instabilities of the system for both repulsive and attractive interaction strengths. To study the response of the system to variations in the rotation rate, we introduce a ``disorder'' potential, breaking the rotational symmetry. We demonstrate the breakdown of adiabaticity as the rotation rate is slowly varied and find forced tunneling between the system's eigenstates. The nonadiabaticity is signaled by the appearance of a swallow-tail loop in the lowest-energy level, a general sign of hysteresis. Then, we show that this system is in one-to-one correspondence with a trapped gas in a double-well potential and thus exhibits macroscopic quantum self-trapping. Finally, we show that self-trapping is a direct manifestation of the behavior of the lowest-energy level.

Shortcuts to adiabaticity in a time-dependent box.

A method is proposed to drive an ultrafast non-adiabatic dynamics of an ultracold gas trapped in a time-dependent box potential. The resulting state is free from spurious excitations associated with the breakdown of adiabaticity, and preserves the quantum correlations of the initial state up to a scaling factor. The process relies on the existence of an adiabatic invariant and the inversion of the dynamical self-similar scaling law dictated by it. Its physical implementation generally requires the use of an auxiliary expulsive potential. The method is extended to a broad family of interacting many-body systems. As illustrative examples we consider the ultrafast expansion of a Tonks-Girardeau gas and of Bose-Einstein condensates in different dimensions, where the method exhibits an excellent robustness against different regimes of interactions and the features of an experimentally realizable box potential.

Non-equilibrium dynamics of O(N) nonlinear sigma models: a large-N approach

We study the time evolution of the mass gap of the O(N) non-linear sigma model in 2+1 dimensions due to a time-dependent coupling in the large-$N$ limit. Using the Schwinger-Keldysh approach, we derive a set of equations at large $N$ which determine the time dependent gap in terms of the coupling. These equations lead to a criterion for the breakdown of adiabaticity for slow variation of the coupling leading to a Kibble-Zurek scaling law. We describe a self-consistent numerical procedure to solve these large-$N$ equations and provide explicit numerical solutions for a coupling which starts deep in the gapped phase at early times and approaches the zero temperature equilibrium critical point $g_c$ in a linear fashion. We demonstrate that for such a protocol there is a value of the coupling $g= g_c^{\rm dyn}> g_c$ where the gap function vanishes, possibly indicating a dynamical instability. We study the dependence of $g_c^{\rm dyn}$ on both the rate of change of the coupling and the initial temperature. We also verify, by studying the evolution of the mass gap subsequent to a sudden change in $g$, that the model does not display thermalization within a finite time interval $t_0$ and discuss the implications of this observation for its conjectured gravitational dual as a higher spin theory in $AdS_4$.

Combined effects of particle interaction and nonlinear sweep on Landau–Zener transition

We investigate the Landau–Zener transition (LZT) of a two-level system with two types of nonlinearity: particle interaction and nonlinear time-dependent energy sweep, both numerically and analytically. Due to the interplay between these two types of nonlinearity, many interesting phenomena in different parameter regions occur, including breakdown of adiabaticity, fade-out of interference phenomenon, and asymmetry of transition probability. The potential experimental observation of transition dynamics in this system is suggested.

Bose-Einstein Condensate in a Honeycomb Optical Lattice: Fingerprint of Superfluidity at the Dirac Point

Mean-field Bloch bands of a Bose-Einstein condensate in a honeycomb optical lattice are computed. We find that the topological structure of the Bloch bands at the Dirac point is changed completely by atomic interaction of arbitrary small strength: the Dirac point is extended into a closed curve and an intersecting tube structure arises around the original Dirac point. These tubed Bloch bands are caused by the superfluidity of the system. Furthermore, they imply the inadequacy of the tight-binding model to describe an interacting Boson system around the Dirac point and the breakdown of adiabaticity by interaction of arbitrary small strength.