We present a general unified approach for the study of quantum thermal machines, including both heat engines and refrigerators, operating under periodic adiabatic driving and in contact with thermal reservoirs kept at different temperatures. We show that many observables characterizing this operating mode and the performance of the machine are of geometric nature. Heat-work conversion mechanisms and dissipation of energy can be described, respectively, by the antisymmetric and symmetric components of a thermal geometric tensor defined in the space of time-dependent parameters generalized to include the temperature bias. The antisymmetric component can be identified as a Berry curvature, while the symmetric component defines the metric of the manifold. We show that the operation of adiabatic thermal machines, and consequently also their efficiency, are intimately related to these geometric aspects. We illustrate these ideas by discussing two specific cases: a slowly driven qubit asymmetrically coupled to two bosonic reservoirs kept at different temperatures, and a quantum dot driven by a rotating magnetic field and strongly coupled to electron reservoirs with different polarizations. Both examples are already amenable for an experimental verification.
We analyze the influence of a dissipative environment on geometric phases in a quantum system subject to non-adiabatic evolution. We find dissipative contributions to the acquired phase and modification of dephasing, considering the cases of weak short-correlated noise as well as of slow quasi-stationary noise. Motivated by recent experiments, we find the leading non-adiabatic corrections to the results, known for the adiabatic limit.
We study the effect of a thermal environment on adiabatic quantum computation using the Bloch-Redfield formalism. We show that in certain cases the environment can enhance the performance in two different ways: (i) by introducing a time scale for thermal mixing near the anticrossing that is smaller than the adiabatic time scale, and (ii) by relaxation after the anticrossing. The former can enhance the scaling of computation when the environment is superohmic, while the latter can only provide a prefactor enhancement. We apply our method to the case of adiabatic Grover search and show that perf…
We propose a theoretical framework that captures the geometric vector potential emerging from the non-adiabatic spin dynamics of itinerant carriers subject to arbitrary magnetic textures. Our approach results in a series of constraints on the geometric potential and the non-adiabatic geometric phase associated with it. These constraints play a decisive role when studying the geometric spin phase gathered by conducting electrons in ring interferometers under the action of in-plane magnetic textures, allowing a simple characterization of the topological transition recently reported by Saarikoski…
We study how the non-adiabatic effect causes the observable fluctuation in the "geometric phase" for a two-level system, which is defined as the experimentally measurable quantity in the adiabatic limit. From the Rabi's exact solution to this model, we give a reasonable explanation to the experimental discovery of phase fluctuation in the superconducting circuit system [P. J. Leek, \textit{et al}., Science \textbf{318}, 1889 (2007)], which seemed to be regarded as the conventional experimental error.
Measurement protocol for non-adiabatic geometric phases of Floquet states
Quantum Advanced Research Center (QuARC), CSIC（量子先进研究中心（QuARC），西班牙国家研究委员会）；Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC（马德里材料科学研究所（ICMM），西班牙国家研究委员会）
We show that geometric phases may be generated in a quantum system subject to noise by adiabatic manipulations of the fluctuating fields, e.g., by variation of the system-environment coupling. For a two-state quantum system we express this phase in terms of the geometry of the path, traversed by the slowly varying direction and amplitude of the fluctuations. We discuss the origin of this phase and possibilities to separate it from the known environment-induced modification of the Berry phase.
We study the role of the quantum geometric tensor (QGT) in the evolution of quantum systems. We show that all its components play an important role on the extra phase acquired by a spinor and on the trajectory of an accelerated wavepacket in any realistic finite-duration experiment. While the adiabatic phase is determined by the Berry curvature (the imaginary part of the tensor), the non-adiabaticity is determined by the quantum metric (the real part of the tensor) and allows to determine corrections in the regimes where Landau-Zener approach is inapplicable. The particular case of a planar mi…
We introduce a self-consistent framework for the analysis of both Abelian and non-Abelian geometric phases associated with open quantum systems, undergoing cyclic adiabatic evolution. We derive a general expression for geometric phases, based on an adiabatic approximation developed within an inherently open-systems approach. This expression provides a natural generalization of the analogous one for closed quantum systems, and we prove that it satisfies all the properties one might expect of a good definition of a geometric phase, including gauge invariance. A striking consequence is the emerge…
We present a unified approach to study continuous measurement based quantum thermal machines in static as well as adiabatically driven systems. We investigate both steady state and transient dynamics for the time-independent case. In the adiabatically driven case, we show how measurement based thermodynamic quantities can be attributed geometric characteristics. We also provide the appropriate definition for heat transfer and dissipation owing to continous measurement in the presence and absence of adiabatic driving. We illustrate the aforementioned ideas and study the phenomena of refrigerati…
The non-adiabatic geometric quantum computation (NGQC) has attracted a lot of attention for noise-resilient quantum control. However, previous implementations of NGQC require long evolution paths that make them more vulnerable to incoherent errors than their dynamical counterparts.In this work, we experimentally realize a universal short-path non-adiabatic geometric gate set (SPNGQC) with a 2-times shorter evolution path on a superconducting quantum processor. Characterizing with both quantum process tomography and randomized benchmarking methods, we report an average single-qubit gate fidelit…
Geometric phases of scattering states in a ring geometry are studied based on a variant of the adiabatic theorem. Three time scales, i.e., the adiabatic period, the system time and the dwell time, associated with adiabatic scattering in a ring geometry plays a crucial role in determining geometric phases, in contrast to only two time scales, i.e., the adiabatic period and the dwell time, in an open system. We derive a formula connecting the gauge invariant geometric phases acquired by time-reversed scattering states and the circulating (pumping) current. A numerical calculation shows that the …
We adopt a geometric approach to describe the performance of adiabatic quantum machines, operating under slow time-dependent driving and in contact to two or more reservoirs with a temperature bias during all the cycle. We show that the problem of optimizing the power generation of a heat engine and the efficiency of both the heat engine and refrigerator operational modes is reduced to an isoperimetric problem with non-trivial underlying metrics and curvature. This corresponds to the maximization of the ratio between the area enclosed by a closed curve and its corresponding length. We illustra…
We consider periodic adiabatic processes of gapped many-body spinless electrons. We find an additional contribution to the orbital magnetization due to the adiabatic time evolution, dubbed \textit{geometric} orbital magnetization, which can be expressed as derivative of the many-body Berry phase with respect to an external magnetic field. For two-dimensional band insulators, we show that the geometric orbital magnetization generally consists of two pieces, the topological piece that is expressed as third Chern-Simons form in $(t,k_x,k_y)$ space, and the non-topological piece that depends on Bl…
Quantum adiabatic pumping of charge and spin between two reservoirs (leads) has recently been demonstrated in nanoscale electronic devices. Pumping occurs when two or more system parameters are varied in a cyclic manner and sufficiently slowly that the quantum system always remains in its ground state. We show that quantum pumping has a natural geometric representation in terms of gauge fields (both Abelian and non-Abelian) defined on the space of system parameters. We make explicit the similarities and differences with Berry's geometric phase. Tunneling from a scanning tunneling microscope ti…
We investigate geometric phase of fermion states under relative vibrations of two sublattices in graphene by solving time-dependent Schödinger equation using Floquet scheme. In a period of vibration the fermions acquire different geometric phases depending on their momenta. There are two regions in the momentum space: the adiabatic region where the geometric phase can be approximated by the Berry phase and the chaotic region where the geometric phase drastically fluctuates in changing parameters. The energy of fermions due to vibrations shows spikes in the chaotic region. The results suggest a…
An electron interferometer was designed and fabricated via a normal metal/insulator/ferromagnet non-local lateral spin valve with a ring-shaped normal metal/insulator spacer, and spin current interference was observed. A very high spin signal of 200 m$Ω$ was found in a device with 2 $μ$m injector-detector distance and magnetic field swept parallel to the plane. With a perpendicular magnetic field sweep, a Hanle effect measurement showed both spin precession and $h/e$ oscillation. Because of the non-adiabatic nature of the precessing spins at low fields as they traverse the normal metal ring, t…
The spin one half molecular system V15 shows no barrier against spin reversal. This makes possible direct phonon activation between the two levels. By tuning the field sweeping rate and the thermal coupling between sample and thermal reservoir we have control over the phonon-bottleneck phenomena previously reported in this system. We demonstrate adiabatic motion of molecule spins in time dependent magnetic fields and with different thermal coupling to the cryostat bath. We also discuss the origin of the zero-field tunneling splitting for a half-integer spin.
We study the adiabatic dynamics of the charge, spin and energy of a quantum dot with a Coulomb interaction under two-parameter driving, associated to time-dependent gate voltage and magnetic field. The quantum dot is coupled to a single reservoir at temperature $T=0$, hence, the net energy dynamics is fully dissipative. However, in the presence of many-body interactions, other interesting mechanisms take place, like the net exchange of work between the two types of forces and the non-equilibrium accumulation of charge with different spin orientations. The latter has a geometric nature. The dis…
In this work we study the geometrical and topological properties of non-equilibrium quantum systems driven by ac fields. We consider two tunnel coupled spin qubits driven by either spatially homogeneous or inhomogeneous ac fields. Our analysis is an extension of the classical model introduced by Berry with he addition of the spatial degree of freedom. We calculate the Berry and Aharonov-Anandan geometric phases, and demonstrate the influence of the different field parameters in the geometric properties. We also discuss the topological properties associated with the different driving regimes, a…
Cyclic Pancharatnam-Berry (PB) and adiabatic noncyclic geometric (ANG) effects are investigated in a single electron orbital system connected to two metal contacts with externally driven chemical potential and/or temperatures.The PB contribution does not affect the density matrix evolution, but has quantitative effect on the statistics (fluctuations) of electron transfer. The ANG contribution, on the other hand, affects the net flux across the junction. Unlike the PB, the ANG contribution is non-zero when two parameters are identically driven. Closed analytical expressions are derived for the …
We study nonadiabatic effects of geometric pumping. With arbitrary choices of periodic control parameters, we go beyond the adiabatic approximation to obtain the exact pumping current. We find that a geometrical interpretation for the nontrivial part of the current is possible even in the nonadiabatic regime. The exact result allows us to find a smooth connection between the adiabatic Berry phase theory at low frequencies and the Floquet theory at high frequencies. We also study how to control the geometric current. Using the method of shortcuts to adiabaticity with the aid of an assisting fie…
Adiabatic pumping is characterized by a geometric contribution to the pumped charge, which can be non-zero even in the absence of a bias. However, as the driving speed is increased, non-adiabatic excitations gradually reduce the pumped charge, thereby limiting the maximal applicable driving frequencies. To circumvent this problem, we here extend the concept of shortcuts to adiabaticity to construct a control protocol which enables geometric pumping well beyond the adiabatic regime. Our protocol allows for an increase, by more than an order of magnitude, in the driving frequencies, and the meth…
We argue that in addition to the Hall conductance and the nondissipative component of the viscous tensor, there exists a third independent transport coefficient, which is precisely quantized. It takes constant values along quantum Hall plateaus. We show that the new coefficient is the Chern number of a vector bundle over moduli space of surfaces of genus 2 or higher and therefore cannot change continuously along the plateau. As such, it does not transpire on a sphere or a torus. In the linear response theory, this coefficient determines intensive forces exerted on electronic fluid by adiabatic…
