The quantum adiabatic theorem, a cornerstone of quantum mechanics, asserts that a gapped quantum system remains in its instantaneous eigenstate during sufficiently slow evolution, provided no resonances occur. Here we challenge this principle and show that adiabaticity can be violated even in arbitrarily slow processes. We introduce two new parameters, Instantaneous Transition Accumulation (ITA) and Instantaneous Transition Probability (ITP), to redefine the framework of adiabatic evolution. These parameters, grounded in cross-Berry connections and eigenstate amplitudes, reveal the dynamic and geometric factors governing adiabaticity. Using a new Phase Difference Manipulation (PDM) method, we control ITP and ITA to induce adiabaticity violation in a Landau-Zener (LZ) process. We experimentally demonstrate this counterintuitive phenomenon in a photonic waveguide system, where a slow LZ process defies adiabaticity, switching energy levels despite a fivefold slower evolution speed than a conventional adiabatic process. This discovery reshapes our understanding of quantum evolution and holds potential for quantum computing, topological physics, and photonic technologies.The quantum adiabatic theorem, a cornerstone of quantum mechanics, asserts that a gapped quantum system remains in its instantaneous eigenstate during sufficiently slow evolution, provided no resonances occur. Here we challenge this principle and show that adiabaticity can be violated even in arbitrarily slow processes. We introduce two new parameters, Instantaneous Transition Accumulation (ITA) and Instantaneous Transition Probability (ITP), to redefine the framework of adiabatic evolution. These parameters, grounded in cross-Berry connections and eigenstate amplitudes, reveal the dynamic and geometric factors governing adiabaticity. Using a new Phase Difference Manipulation (PDM) method, we control ITP and ITA to induce adiabaticity violation in a Landau-Zener (LZ) process. We experimentally demonstrate this counterintuitive phenomenon in a photonic waveguide system, where a slow LZ process defies adiabaticity, switching energy levels despite a fivefold slower evolution speed than a conventional adiabatic process. This discovery reshapes our understanding of quantum evolution and holds potential for quantum computing, topological physics, and photonic technologies.

arXiv:2506.02681Jun 3, 20250 citations

Hierarchical theory of quantum adiabatic evolution

Qi Zhang, Jiangbin Gong, Biao Wu

Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between nondegenerate instantaneous energy eigenstates in such a dynamical evolution. However, this is true only when the driving rate is infinitesimally small. For a small nonzero driving rate, there are generally small transition probabilities between the energy eigenstates. We develop a classical mechanics framework to address the small deviations from the quantum adiabatic theorem order by order. A hierarchy of Hamiltonians is constructed iteratively with the zeroth-order Hamiltonian being determined by the original system Hamiltonian. The k th-order deviations are governed by a k th-order Hamiltonian, which depends on the time derivatives of the adiabatic parameters up to the k th-order. Two simple examples, the Landau–Zener model and a spin-1/2 particle in a rotating magnetic field, are used to illustrate our hierarchical theory. Our analysis also exposes a deep, previously unknown connection between classical adiabatic theory and quantum adiabatic theory.Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between nondegenerate instantaneous energy eigenstates in such a dynamical evolution. However, this is true only when the driving rate is infinitesimally small. For a small nonzero driving rate, there are generally small transition probabilities between the energy eigenstates. We develop a classical mechanics framework to address the small deviations from the quantum adiabatic theorem order by order. A hierarchy of Hamiltonians is constructed iteratively with the zeroth-order Hamiltonian being determined by the original system Hamiltonian. The k th-order deviations are governed by a k th-order Hamiltonian, which depends on the time derivatives of the adiabatic parameters up to the k th-order. Two simple examples, the Landau–Zener model and a spin-1/2 particle in a rotating magnetic field, are used to illustrate our hierarchical theory. Our analysis also exposes a deep, previously unknown connection between classical adiabatic theory and quantum adiabatic theory.

arXiv:1402.6431New Journal of PhysicsDec 10, 20146 citations

Breaking the quantum adiabatic speed limit by jumping along geodesics

Kebiao Xu, Tianyu Xie, Fazhan Shi +6 more

Quantum adiabatic evolutions find a broad range of applications in quantum physics and quantum technologies. The traditional form of the quantum adiabatic theorem limits the speed of adiabatic evolution by the minimum energy gaps of the system Hamiltonian. Here, we experimentally show using a nitrogen-vacancy center in diamond that, even in the presence of vanishing energy gaps, quantum adiabatic evolution is possible. This verifies a recently derived necessary and sufficient quantum adiabatic theorem and offers paths to overcome the conventionally assumed constraints on adiabatic methods. By fast modulation of dynamic phases, we demonstrate near-unit-fidelity quantum adiabatic processes in finite times. These results challenge traditional views and provide deeper understanding on quantum adiabatic processes, as well as promising strategies for the control of quantum systems.Quantum adiabatic evolutions find a broad range of applications in quantum physics and quantum technologies. The traditional form of the quantum adiabatic theorem limits the speed of adiabatic evolution by the minimum energy gaps of the system Hamiltonian. Here, we experimentally show using a nitrogen-vacancy center in diamond that, even in the presence of vanishing energy gaps, quantum adiabatic evolution is possible. This verifies a recently derived necessary and sufficient quantum adiabatic theorem and offers paths to overcome the conventionally assumed constraints on adiabatic methods. By fast modulation of dynamic phases, we demonstrate near-unit-fidelity quantum adiabatic processes in finite times. These results challenge traditional views and provide deeper understanding on quantum adiabatic processes, as well as promising strategies for the control of quantum systems.

arXiv:1711.02911Science AdvancesJun 1, 201930 citations

General conditions for quantum adiabatic evolution

D. Comparat

Adiabaticity occurs when, during its evolution, a physical system remains in the instantaneous eigenstate of the Hamiltonian. Unfortunately, existing results, such as the quantum adiabatic theorem based on a slow down evolution $[H(ϵt),ϵ\ensuremath{\rightarrow}0]$, are insufficient to describe an evolution driven by the Hamiltonian $H(t)$ itself. Here we derive general criteria and exact bounds, for the state and its phase, ensuring an adiabatic evolution for any Hamiltonian $H(t)$ . As a corollary, we demonstrate that the commonly used condition of a slow Hamiltonian variation rate, compared to the spectral gap, is indeed sufficient to ensure adiabaticity but only when the Hamiltonian is real and nonoscillating (for instance, containing exponential or polynomial but no sinusoidal functions).Adiabaticity occurs when, during its evolution, a physical system remains in the instantaneous eigenstate of the Hamiltonian. Unfortunately, existing results, such as the quantum adiabatic theorem based on a slow down evolution $[H(ϵt),ϵ\ensuremath{\rightarrow}0]$, are insufficient to describe an evolution driven by the Hamiltonian $H(t)$ itself. Here we derive general criteria and exact bounds, for the state and its phase, ensuring an adiabatic evolution for any Hamiltonian $H(t)$. As a corollary, we demonstrate that the commonly used condition of a slow Hamiltonian variation rate, compared to the spectral gap, is indeed sufficient to ensure adiabaticity but only when the Hamiltonian is real and nonoscillating (for instance, containing exponential or polynomial but no sinusoidal functions).

arXiv:quant-ph/0607118Physical Review AJul 15, 200993 citations

Counterdiabatic driving for random-gap Landau-Zener transitions

Georgios Theologou, Mikkel F. Andersen, Sandro Wimberger

The Landau--Zener (LZ) model describes a two-level quantum system that undergoes an avoided crossing. In the adiabatic limit, the transition probability vanishes. An auxiliary control field $H_\text{CD}$ can be reverse-engineered so that the full Hamiltonian $H_0 + H_\text{CD}$ reproduces adiabaticity for all parameter values. Our aim is to construct a single control field $H_1$ that drives an ensemble of LZ-type Hamiltonians with a distribution of energy gaps. $H_1$ works best statistically, minimizing the average transition probability. We restrict our attention to a special class of $H_1$ controls, motivated by $H_\text{CD}$ . We found a systematic trade-off between instantaneous adiabaticity and the final transition probability. Certain limiting cases with a linear sweep can be treated analytically; one of them being the LZ system with Dirac $δ(t)$ function. Comprehensive and systematic numerical simulations support and extend the analytic results.The Landau--Zener (LZ) model describes a two-level quantum system that undergoes an avoided crossing. In the adiabatic limit, the transition probability vanishes. An auxiliary control field $H_\text{CD}$ can be reverse-engineered so that the full Hamiltonian $H_0 + H_\text{CD}$ reproduces adiabaticity for all parameter values. Our aim is to construct a single control field $H_1$ that drives an ensemble of LZ-type Hamiltonians with a distribution of energy gaps. $H_1$ works best statistically, minimizing the average transition probability. We restrict our attention to a special class of $H_1$ controls, motivated by $H_\text{CD}$. We found a systematic trade-off between instantaneous adiabaticity and the final transition probability. Certain limiting cases with a linear sweep can be treated analytically; one of them being the LZ system with Dirac $δ(t)$ function. Comprehensive and systematic numerical simulations support and extend the analytic results.

quant-pharXiv:2601.10659Journal of Physics A Mathematical and TheoreticalJan 16, 20261 citation

Eigenstate tracking in open quantum systems

Jun Jing, M. S. Sarandy, Daniel A. Lidar +2 more

Keeping a quantum system in a given instantaneous eigenstate is a control problem with numerous applications, e.g., in quantum information processing. The problem is even more challenging in the setting of open quantum systems, where environment-mediated transitions introduce additional decoherence channels. Adiabatic passage is a well-established solution but requires a sufficiently slow evolution time that is dictated by the adiabatic theorem. Here we develop a systematic projection theory formulation for the transitionless evolution of general open quantum systems described by time-local master equations. We derive a time-convolutionless dynamical equation for the target instantaneous eigenstate of a given time-dependent Hamiltonian. A transitionless dynamics then arises in terms of a competition between the average Hamiltonian gap and the decoherence rate, which implies optimal adiabaticity timescales. We show how eigenstate tracking can be accomplished via control pulses, without explicitly incorporating counter-diabatic driving, thus offering an alternative route to accelerate adiabaticity. We examine rectangular pulses, chaotic signals, and white noise, and find that, remarkably, the effectiveness of eigenstate tracking hardly depends on the details of the control functions. In all cases the control protocol keeps the system in the desired instantaneous eigenstate throughout the entire evolution, along an accelerated adiabatic path.Keeping a quantum system in a given instantaneous eigenstate is a control problem with numerous applications, e.g., in quantum information processing. The problem is even more challenging in the setting of open quantum systems, where environment-mediated transitions introduce additional decoherence channels. Adiabatic passage is a well-established solution but requires a sufficiently slow evolution time that is dictated by the adiabatic theorem. Here we develop a systematic projection theory formulation for the transitionless evolution of general open quantum systems described by time-local master equations. We derive a time-convolutionless dynamical equation for the target instantaneous eigenstate of a given time-dependent Hamiltonian. A transitionless dynamics then arises in terms of a competition between the average Hamiltonian gap and the decoherence rate, which implies optimal adiabaticity timescales. We show how eigenstate tracking can be accomplished via control pulses, without explicitly incorporating counter-diabatic driving, thus offering an alternative route to accelerate adiabaticity. We examine rectangular pulses, chaotic signals, and white noise, and find that, remarkably, the effectiveness of eigenstate tracking hardly depends on the details of the control functions. In all cases the control protocol keeps the system in the desired instantaneous eigenstate throughout the entire evolution, along an accelerated adiabatic path.

arXiv:1605.07523Physical Review AOct 28, 201631 citations

H(t)

itself. Here we derive general criteria and exact bounds, for the state and its phase, ensuring an adiabatic evolution for any Hamiltonian

H(t)

. As a corollary, we demonstrate that the commonly used condition of a slow Hamiltonian variation rate, compared to the spectral gap, is indeed sufficient to ensure adiabaticity but only when the Hamiltonian is real and nonoscillating (for instance, containing exponential or polynomial but no sinusoidal functions).

The Landau--Zener (LZ) model describes a two-level quantum system that undergoes an avoided crossing. In the adiabatic limit, the transition probability vanishes. An auxiliary control field

H_\text{CD}

can be reverse-engineered so that the full Hamiltonian

H_0 + H_\text{CD}

reproduces adiabaticity for all parameter values. Our aim is to construct a single control field

H_1

that drives an ensemble of LZ-type Hamiltonians with a distribution of energy gaps.

H_1

works best statistically, minimizing the average transition probability. We restrict our attention to a special class of

H_1

controls, motivated by

H_\text{CD}

. We found a systematic trade-off between instantaneous adiabaticity and the final transition probability. Certain limiting cases with a linear sweep can be treated analytically; one of them being the LZ system with Dirac

δ(t)

function. Comprehensive and systematic numerical simulations support and extend the analytic results.