We study the quantum dynamics of a two-level system driven by a pulse that starts near-resonant for small amplitudes, yielding nonadiabatic evolution, and induces an adiabatic evolution for larger amplitudes. This problem is analyzed in terms of lifting of degeneracy for rising amplitudes. It is solved exactly for the case of linear and exponential rising. Approximate solutions are given in the case of power law rising. This allows us to determine approximative formulas for the lineshape of resonant excitation by various forms of pulses such as truncated trig-pulses. We also analyze and explain the various superpositions of states that can be obtained by the Half Stark Chirped Rapid Adiabatic Passage (Half-SCRAP) process.
There are two well known mechanisms which lead to lifting of energy spin degeneracy of single electron systems - magnetic field and spin-orbit coupling. We investigate the possibility for existence of a third mechanism in which electrostatic field can lead to lifting of spin-degeneracy directly without the mediation of spin-orbit coupling. A novel argument is provided for the need of spin-orbit coupling different from the usual relativistic considerations. It is shown that due to preserved translational invariance spin splitting purely by electrostatic field is not possible for Bloch states. A…
We investigate the symmetry breaking role of noise in adiabatic quantum computing using the example of the CNOT gate. In particular, we analyse situations where the choice of initial configuration leads to symmetries in the Hamiltonian and degeneracies in the spectrum. We show that, in these situations, there exists an optimal level of noise that maximises the success probability and the fidelity of the final state. The effects of an artificial noise source with a time-dependent amplitude are also explored and it is found that such a scheme would offer a considerable performance enhancement.
A classical-kind phase-space formalism is developed to address the tiny intrinsic dynamical deviation from what is predicted by Wilczek-Zee theorem during quantum adiabatic evolution on degeneracy levels. In this formalism, the Hilbert space and the aggregate of degenerate eigenstates become the classical-kind phase-space and a high-dimensional subspace in the phase-space, respectively. Compared with the previous same study by a different method, the current result is qualitatively different in that the first-order deviation derived here is always perpendicular to the degeneracy subspace. A tr…
Long-lived and high-fidelity memory for photonic polarization qubit (PPQ) is crucial for constructing quantum networks. Here we present an EIT-based millisecond storage system in which a moderate magnetic field is applied on a cold-atom cloud to lift Zeeman degeneracy. PPQ states are stored as two magnetic-field-insensitive spin waves. Especially, the influence of magnetic-field-sensitive spin waves on the storage performances is almost totally avoided. The measured average fidelities of polarization states are 98.6% at 200 us and 78.4% at 4.5 ms, respectively.
In quantum information, lifting is a systematic procedure that can be used to derive---when provided with a seed Bell inequality---other Bell inequalities applicable in more complicated Bell scenarios. It is known that the procedure of lifting introduced by Pironio [J. Math. Phys. A 46, 062112 (2005)] preserves the facet-defining property of a Bell inequality. Lifted Bell inequalities therefore represent a broad class of Bell inequalities that can be found in {\em all} Bell scenarios. Here, we show that the maximal value of {\em any} lifted Bell inequality is preserved for both the set of nons…
By stating the adiabatic theorem of quantum mechanics in a clear and rigorous way, we establish a necessary condition and a sufficient condition for its validity, where the latter is obtained employing our recently developed adiabatic perturbation theory. Also, we simplify further the sufficient condition into a useful and simple practical test at the expenses of its mathematical rigor. We present results for the most general case of quantum systems, i.e., those with degenerate energy spectra. These conditions are of upmost importance to assess the validity of practical implementations of non-…
We decompose the quantum adiabatic evolution as the products of gauge invariant unitary operators and obtain the exact nonadiabatic correction in the adiabatic approximation. A necessary and sufficient condition that leads to adiabatic evolution with geometric phases is provided and we determine that in the adiabatic evolution, while the eigenstates are slowly varying, the eigenenergies and degeneracy of the Hamiltonian can change rapidly. We exemplify this result by the example of the adiabatic evolution driven by parametrized pulse sequences. For driving fields that are rotating slowly with …
Exceptional points, the spectral degeneracy points in the complex parameter space, are fundamental to non-Hermitian quantum systems. The dynamics of non-Hermitian systems in the presence of exceptional points differ significantly from those of Hermitian ones. Here we investigate non-adiabatic transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric systems, in which the exceptional points are driven through at finite speed which are quadratic or cubic functions of time. We identity different transmission dynamics separated by exceptional points, and derive analytical approximate formula…
The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with $N$-fold degeneracy. The corresponding geometric phase is interpreted as a holonomy inherited from the universal connection of a Stiefel U(N)-bundle over a Grassmann manifold. Most significantly, for an arbitrary initial state, this geometric phase captures the inherent geometric feature of the state evolution. Moreover, the geometric phase in the evolution of the eigenspace of an adiabatic action operator is also addressed, which is elaborated by a pullback U(N)-bundle. Several i…
We present a quantum algorithm for implementing $ϕ^4$ lattice scalar field theory on qubit computers. The field is represented in the discretized field amplitude basis. The number of qubits and elementary gates required by the implementation of the evolution operator is proportional to the lattice size. The algorithm allows efficient $ϕ^4$ state preparation for a large range of input parameters in both the normal and broken-symmetry phases. The states are prepared using a combination of variational and adiabatic evolution methods. First, the ground state of a local Hamiltonian, which includes …
A novel mechanism is proposed for single and double qubit state manipulations in quantum computation with four-fold degenerate energy levels. The principle is based on starting with a four fold degeneracy, lifting it stepwise adiabatically by a set of control parameters and performing the quantum gate operations on non-degenerate states. A particular realization of the proposed mechanism is suggested by using inductively coupled rf-squid loops in the macroscopic quantum tunnelling regime where the energy eigen levels are directly connected with the measurable flux states. The one qubit and two…
We examine the conditions needed to accomplish stimulated Raman adiabatic passage (STIRAP) when the three levels (g, e and f) are degenerate, with arbitrary couplings contributing to the pump-pulse interaction (g - e) and to the Stokes-pulse interaction (e-f). We show that in general a sufficient condition for complete population removal from the g set of degenerate states for arbitrary, pure or mixed, initial state is that the degeneracies should not decrease along the sequence g, e and f. We show that when this condition holds it is possible to achieve the degenerate counterpart of conventio…
An asymptotic approach for a Schroedinger type equation with a non selfadjoint slowly varying Hamiltonian of a special type is developed. The Hamiltonian is assumed to be the result of a small perturbation of an operator with a twofold degeneracy (turning) point, which can be diagonalized at this point. The non-adiabatic transformation of modes is studied in the case where two small parameters are dependent: the parameter characterizing an order of the perturbation is a square root of the adiabatic parameter. The perturbation of the Hamiltonian produces a close pair of simple degeneracy points…
The hydrogen bond is usually described within the clamped nucleus approximation in which electronic and vibrational motions are considered separately. This approach leads to a double-well potential which facilitates proton tunnelling. In this work, the hydrogen bond is described by a formalism based on the non-adiabatic Hamiltonian in which electronic and vibrational motions are coupled. Quasi-degeneracy associated with the hydrogen bond supports this approach which is shown to afford an alternative picture of proton tunnelling.
We show in this Letter that the ground state degeneracy associated with the presence of non-Abelian anyons can be probed by using an adiabatic cooling process based on the non-Abelian entropy. In particular, we show that when the number of such anyons is increased adiabatically at sufficiently low temperatures, the non-Abelian liquid undergoes cooling, whereas heating occurs in the Abelian case. Estimates are provided for the cooling power produced by the non-Abelian anyon refrigerator, and its implementation in non-Abelian fractional quantum Hall liquids is discussed.
The ground state susceptibility of a system consisting of three flux-qubits was measured in the complete three dimensional flux space around the common degeneracy point of the qubits. The system's Hamiltonian could be completely reconstructed from measurements made far away from the common degeneracy point. The subsequent measurements made around this point show complete agreement with the theoretical predictions which follow from this Hamiltonian. The ground state anti-crossings of the system could be read-out directly from these measurements. This allows one to determine the ground-state flu…
An adiabatic change of a bound state along a closed circuit in the parameter space can induces holonomies not only in the phase of the state, but also in the associated eigenspace and eigenvalue. The former is the well-known Berry phase while the latter, namely the exotic holonomy, is found a decade ago and its origin has not been understood yet. By extending the parameter into the complex number, the correspondence of the exotic holonomies and the degeneracy of the non-Hermitian Hamiltonian, or the exceptional points, is revealed. We show that this explains all the known non-trivial character…
Delta kick cooling (DKC) is used to compress the momentum distribution of ultracold quantum matter. It combines expansion dynamics with the use of kick pulses, designed via classical methods, that bring the system to rest. We introduce an exact approach to DKC for arbitrary scale-invariant dynamics of quantum gases, lifting the original restrictions to free evolution and noninteracting systems, to account for the control of atomic clouds in a time-dependent harmonic trap that can be either repulsive (inverted) or confining. We show that DKC assisted by a repulsive potential outperforms the con…
We study the approach to the adiabatic limit in periodically driven systems. Specifically focusing on a spin-1/2 in a magnetic field we find that, when the parameters of the Hamiltonian lead to a quasi-degeneracy in the Floquet spectrum, the evolution is not adiabatic even if the frequency of the field is much smaller than the spectral gap of the Hamiltonian. We argue that this is a general phenomenon of periodically driven systems. Although an explanation based on a perturbation theory in $ω_0$ cannot be given, because of the singularity of the zero frequency limit, we are able to describe th…
We elucidate the geometry of quantum adiabatic evolution. By minimizing the deviation from adiabaticity we find a Riemannian metric tensor underlying adiabatic evolution. Equipped with this tensor, we identify a unified geometric description of quantum adiabatic evolution and quantum phase transitions, which generalizes previous treatments to allow for degeneracy. The same structure is relevant for applications in quantum information processing, including adiabatic and holonomic quantum computing, where geodesics over the manifold of control parameters correspond to paths which minimize errors…
We investigate superradiant-like dynamics of the nuclear-spin bath in a single-electron quantum dot, by considering electrons cyclically shuttling on/off an isotopically enriched `nuclear-spin island'. Assuming a uniform hyperfine interaction, we discuss in detail the nuclear spin evolution under shuttling and its relation to superradiance. We derive the minimum shuttling time which allows to escape the adiabatic spin evolution. Furthermore, we discuss slow/fast shuttling under the inhomogeneous field of a nearby micromagnet. Finally, by comparing our scheme to a model with stationary quantum …
An adiabatic cycle of parameters in a quantum system can yield the quantum anholonomies, nontrivial evolution not just in phase of the states, but also in eigenvalues and eigenstates. Such exotic anholonomies imply that an adiabatic cycle rearranges eigenstates even without spectral degeneracy. We show that an arbitrarily large quantum circuit generated by recursive extension can also exhibit the eigenvalue and eigenspace anholonomies.
Quantum phase transitions materialize as level crossings in the ground-state energy when the parameters of the Hamiltonian are varied. The resulting ground-state phase diagrams are straightforward to determine by exact diagonalization on classical computers, but are challenging on quantum computers because of the accuracy needed and the near degeneracy of competing states close to the level crossings. In this work, we use a local adiabatic ramp for state preparation to allow us to directly compute ground-state phase diagrams on a quantum computer via time evolution. This methodology is illustr…
Two recent preprints [B. Altshuler, H. Krovi, and J. Roland, "Quantum adiabatic optimization fails for random instances of NP-complete problems", arXiv:0908.2782 and "Anderson localization casts clouds over adiabatic quantum optimization", arXiv:0912.0746] argue that random 4th order perturbative corrections to the energies of local minima of random instances of NP-complete problem lead to avoided crossings that cause the failure of quantum adiabatic algorithm (due to exponentially small gap) close to the end, for very small transverse field that scales as an inverse power of instance size N. …
