We provide provide a detailed study of biasless coherent transport of singlet electron pairs in one-dimensional (1D) channels induced by electron-electron interactions that are time-varying in certain spatially localized regions of the channel. When the time variation is cyclic, the mechanism is analogous to the adiabatic quantum pumping of charge and spin previously studied. However, the presence of interactions that vary only in localized regions of space requires an intrinsically two-body description which is irreducible to the 1D single particle scattering matrix elements that are sufficient to describe quantum pumping of charge and spin. Here we derive a generalized theory for the pumping of such interacting pairs starting from first principles. We show that the standard description of charge pumping is contained within our more broadly applicable expressions. We then apply our general results to a concrete lattice model and obtain an exact analytical expression for the pumped singlet current. We further demonstrate that such a model can be implemented with a chain of currently available quantum dots with certain minor modifications that we suggest; we present a detailed numerical feasibility analysis of the characteristics of such experimentally realizable quantum dots, showing that the requirements for a measurable pumped singlet current are within experimental range.
We provide provide a detailed study of biasless coherent transport of singlet electron pairs in one-dimensional (1D) channels induced by electron-electron interactions that are time-varying in certain spatially localized regions of the channel. When the time variation is cyclic, the mechanism is analogous to the adiabatic quantum pumping of charge and spin previously studied. However, the presence of interactions that vary only in localized regions of space requires an intrinsically two-body description which is irreducible to the 1D single particle scattering matrix elements that are sufficient to describe quantum pumping of charge and spin. Here we derive a generalized theory for the pumping of such interacting pairs starting from first principles. We show that the standard description of charge pumping is contained within our more broadly applicable expressions. We then apply our general results to a concrete lattice model and obtain an exact analytical expression for the pumped singlet current. We further demonstrate that such a model can be implemented with a chain of currently available quantum dots with certain minor modifications that we suggest; we present a detailed numerical feasibility analysis of the characteristics of such experimentally realizable quantum dots, showing that the requirements for a measurable pumped singlet current are within experimental range.
We propose a method to dynamically generate and control the flow of spin-entangled electrons, each belonging to a spin singlet, by means of adiabatic quantum pumping. The pumping cycle functions by periodic time variation of localized two-body interactions. We develop a generalized approach to adiabatic quantum pumping as traditional methods based on a scattering matrix in one dimension cannot be applied here. We specifically compute the flow of spin-entangled electrons within a Hubbard-like model of quantum dots, discuss possible implementations, and identify parameters that can be used to control the singlet flow.
The adiabatic charge pumping of a nonequilibrium state of spinless fermions in a one-dimensional lattice is investigated, with an emphasis placed on its usefulness in revealing many-body interaction effects on interband coherence. For a noninteracting system, the pumped charge per adiabatic cycle depends not only on the topology of the occupied bands but also on the interband coherence in the initial state. This insight leads to an interesting opportunity for quantitatively observing how quantum coherence is affected by many-body interaction that is switched on for a varying duration prior to adiabatic pumping. In particular, interband coherence effects can be clearly observed by adjusting the switch-on rates with different adiabatic pumping protocols and by scanning the duration of many-body interaction prior to adiabatic pumping. The time dependence of single-particle interband coherence in the presence of many-body interaction can then be examined in detail. As an interesting side result, for relatively weak interaction strength, it is found that the difference in the pumped charges between different pumping protocols vanishes if a coherence measure defined by the single-particle density matrix in the sublattice representation reaches its local minima. Our results hence provide an interesting means to quantitatively probe the dynamics of quantum coherence in the presence of many-body interaction (e.g., in a thermalization process).
Abstract The understanding of out-of-equilibrium fluctuation relations in small open quantum systems has been a focal point of research in recent years. In particular, for systems with adiabatic time-dependent driving, it was shown that the fluctuation relations known from stationary systems do no longer apply due the geometric nature of the pumping current response. However, the precise physical interpretation of the corrected pumping fluctuation relations as well as the role of many-body interactions remained unexplored. Here, we study quantum systems with many-body interactions subject to slow time-dependent driving, and show that fluctuation relations of the charge current can in general not be formulated without taking into account the total energy current put into the system through the pumping process. Moreover, we show that this correction due to the input energy is nonzero only when Coulomb-interactions are present. Thus, fluctuation response relations offer an until now unrevealed opportunity to probe many-body correlations in quantum systems. We demonstrate our general findings at the concrete example of a single-level quantum dot model, and propose a scheme to measure the interaction-induced discrepancies from the stationary case.
A two-level quantum system is the building block of a quantum computer. This pair of quantum states defines the computational unit of a quantum computer, and it is called a quantum bit or qubit in analogy to the bit that is the binary unit of a classical computer. The spin of a single electron naturally defines such a two-level quantum system. A quantum dot can be tuned to the single-electron regime, and an array of singly occupied quantum dots provides a multi-qubit register. This thesis describes the multielectron encoding of a spin qubit using a pair or a trio of quantum dots, and it analyzes the coherence properties and manipulation protocols of this system. The singlet-triplet qubit, coded using the singlet state and the spinless triplet state of a pair of singly occupied quantum dots, can be controlled all electrically when applying voltages to gates close to the quantum dot structure. Rapid, subnanosecond modifications of the double quantum dot's charge configuration have been realized successfully. A small magnetic field gradient across the double quantum dot enables universal qubit control. Two modifications of the normal singlet-triplet encoding are introduced. (1) The six-electron configuration of a double quantum dot encodes a singlet-triplet qubit in the same way as for the two-electron double quantum dot. Two electrons at each quantum dot are irrelevant for the qubit manipulations because they are paired in a singlet state; the remaining two electrons encode the qubit. The qubit's wave function is immune to charge noise at moderate out-of-plane magnetic fields. (2) A singlet-triplet qubit encoded using two quantum dots of different sizes has an orbital state degeneracy of the singlet state and the spinless triplet state at finite out-of-plane magnetic fields. Spin-orbit interactions lift this state degeneracy, while the magnitude of the state coupling is determined by the size difference of the QDs. This setup enables the manipulations of singlet-triplet qubits without the need for magnetic field gradients. Finally, two-qubit gates between singlet-triplet qubits are proposed that use mediated exchange interactions via one quantum state. These operations are well controlled and highly noise insensitive. Orbital interactions alone can control spin qubits coded in a three electron Hilbert space. For example, the exchange-only qubit is encoded using three singly occupied quantum dots. The exchange interactions of two quantum dot pairs need to be modified to manipulate this qubit. The noise sensitivity of the exchange-only qubit is discussed. Alternatively, a three-electron qubit at a double quantum dot can be operated when single electrons are transferred between the quantum dots. Fast, subnanosecond manipulations of the double quantum dot's charge configuration are required to realize single-qubit gates. A novel two-qubit pulse gate for the three-electron double quantum dot qubit is proposed.
A dc current can be pumped through an interacting system by periodically varying two independent parameters such as the magnetic field and a gate potential. We present a general expression for the adiabatic pumping current in interacting systems, written in terms of instantaneous properties of the system at equilibrium, and find the limits of its applicability. This expression generalizes the scattering approach for noninteracting particles. We apply our formula for a quantum critical system that exhibits the two-channel Kondo effect, where single particle excitations are not well defined. We find that if the quantum critical point is contained in the pumping trajectory, the pumped spin between the channels approaches h, and if it is not contained in the trajectory, the spin approaches zero when the temperature T --> 0. We discuss the non-Fermi liquid features of this system at finite T.
The implementation and characterization of minimal instances of complex many-body systems have fundamental importance for the development of quantum simulators. This thesis reports on the implementation of two such minimal instances: a minimal instance for ℤ₂ lattice gauge theories coupled to matter and a minimal instance for spin pumping. ℤ₂ lattice gauge theories are characterized by a ℤ₂ gauge degree-of-freedom on every lattice link. Matter particles moving across these links pick up a phase depending on the traversed link's gauge field. To conserve the local gauge symmetry during this motion, also the gauge field itself changes. A corresponding minimal instance consists of a single matter particle on two lattice sites, which are connected by a link. The presented implementation of this minimal instance is based on two-component ultracold rubidium atoms in a periodically-driven optical double-well potential with a state-dependent energy offset between neighboring sites. In this implementation, one component represents the matter, while the other component represents the gauge field. The resulting effective Floquet Hamiltonian exhibits ℤ₂ symmetry for specific modulation parameters, if the periodic driving is resonant with the on-site interaction energy. The dynamics was investigated for different initial states and compared to a numerical analysis. This numerical analysis is in agreement with the measurements and reveals nontrivial dynamics as expected from a ℤ₂ lattice gauge theory coupled to matter. Furthermore, symmetry-breaking terms are identified and routes to overcome these limitations are discussed. Finally, a way to couple minimal instances to a one-dimensional extended system is proposed. The results constitute a first step towards quantum simulation of gauge theories and provide important insights for future studies using Floquet-based techniques. A quantum spin pump generates a spin transport in response to a cyclic and adiabatic variation of a one-dimensional Hamiltonian. The spins are transported in opposite directions and thereby exhibit a vanishing charge transport. In a spin-conserving system with homogeneously filled bands, the spin transport per pump cycle is quantized and deeply connected to the pump cycle's topology. Therefore, such a spin pump can be interpreted as a dynamical version of a two-dimensional time-reversal symmetric quantum spin Hall system. In the experiment, a minimal instance of such a spin pump was implemented with ultracold rubidium atoms in an optical double-well potential. In the limit of piecewise isolated instances throughout the pump cycle, where each instance shifts by one lattice site per half pump cycle, a one-dimensional spin pump is realized. To characterize the response of the pump, the spin separation and the occurring spin currents are measured. For the detection of the spin separation, the center-of-mass positions of both spin components are analyzed in in-situ absorption images. For the detection of spin currents, a novel detection method was developed, which connects the superexchange oscillations after a projection onto static double wells to the instantaneous spin current. This newly developed method can be applied to a general class of systems and in combination with single-site detection, it also allows for a local detection of instantaneous spin currents. The results demonstrate a corner stone for the implementation of a spin pump, which can be extended, e.g. by adding time-reversal-invariant spin--orbit interactions or by breaking time-reversal symmetry. This extension then results either in a system described by a nontrivial ℤ₂ invariant or a quantum spin Hall system described by a spin-Chern number.