One of the challenges of adiabatic control theory is the proper inclusion of the effects of dissipation. Here we study the adiabatic dynamics of an open two-level quantum system deriving a generalized master equation to consistently account for the combined action of the driving and dissipation. We demonstrate that in the zero-temperature limit the ground state dynamics is not affected by environment. As an example, we apply our theory to Cooper pair pumping, which demonstrates the robustness of ground state adiabatic evolution.

We present a measurement scheme for observing the Berry phase in a flux assisted Cooper pair pump - the Cooper pair sluice. In contrast to the recent experiments, in which the sluice was employed to generate accurate current through a resistance, we consider a device in a superconducting loop. This arrangement introduces a connection between the pumped current and the Berry phase accumulated during the adiabatic pumping cycles. From the adiabaticity criterion, we derive equations for the maximum pumped current and optimize the sluice accordingly. These results apply also to the high accuracy pumping which results in a potential candidate for a metrological current standard. For measuring the pumped current, an additional Josephson junction is installed into the superconducting loop. We show in detail that the switching of this system from superconducting state into normal state as a consequence of an external current pulse through it may be employed to probe the pumped current. The experimental realization of our scheme would be the first observation of the Berry phase in superconducting circuits.Comment: 19 pages, 5 figure

We discuss the transport properties of a disordered two-dimensional electron gas with strong Rashba spin-orbit coupling. We show that in the high-density regime where the Fermi energy overcomes the energy associated with spin-orbit coupling, dc transport is accurately described by a standard Drude's law, due to a nontrivial compensation between the suppression of backscattering and the relativistic correction to the quasiparticle velocity. On the contrary, when the system enters the opposite dominant spin-orbit regime, Drude's paradigm breaks down and the dc conductivity becomes strongly sensitive to the spin-orbit coupling strength, providing a suitable tool to test the entanglement between spin and charge degrees of freedom in these systems. DOI: 10.1103/PhysRevLett.116.166602 Spin-orbit (SO) coupling is a fundamental ingredient in spintronics [1], as it provides an advantageous locking between spin and electron orbital momentum. Recently, intense research efforts [2] have been devoted to twodimensional materials with broken inversion symmetry, where the SO strength, parametrized by a characteristic energy scale E 0 , can be tuned by means of external conditions (electric fields, gating, doping, pressure, strain, etc.). In most of these systems (for example, surface alloys [3][4][5][6][7][8][9], layered bismuth tellurohalides [10][11][12][13][14][15][16], HgTe quantum wells [17], and interfaces between complex oxides [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]) the total charge carrier density n can be tuned down to very small concentrations, implying very small Fermi energies E F . Although the high-density (HD) regime E F ≳ E 0 has been widely investigated [2,[33][34][35][36][37][38], relatively less attention has been paid to the opposite regime of dominant SO (DSO), E 0 ≳ E F .In this Letter we provide a detailed investigation of the dc conductivity of a 2D electron gas (2DEG) with Rashba [39] SO coupling in the different density regimes. Using a Boltzmann approach and a fully quantum analysis based on the Kubo formula, we show that in the high-density regime E F ≳ E 0 dc transport is independent of the SO strength, and the dc conductivity σ dc of electrons having effective mass m and scattering time τ 0 follows the conventional Drude law for 2DEGs,which results from a nontrivial cancellation of the SO coupling effects on the quasiparticle velocity and transport scattering time. Remarkably, as soon as the system enters the DSO regime E 0 ≳ E F , Drude's paradigm Eq. (1) breaks down and the dc conductivity accurately follows the analytical formula:where n 0 ¼ 2mE 0 =ðπℏ 2 Þ is the density at E F ¼ E 0 . In contrast to the linear dependence of σ dc on the charge density found in the HD regime, n ≥ n 0 , Eq. (2) predicts an unconventional nonlinear behavior of σ dc with n that is controlled by the SO interaction encoded in n 0 . The relevance of this result is twofold: demonstrating that dc transport is strongly sensitive to Rashba SO coupling, not only does it suggest that SO coupling cou...

We demonstrate that hexagonal graphene nanoflakes with zigzag edges display quantum interference (QI) patterns analogous to benzene molecular junctions. In contrast with graphene sheets, these nanoflakes also host magnetism. The cooperative effect of QI and magnetism enables spin-dependent quantum interference effects that result in a nearly complete spin polarization of the current and holds a huge potential for spintronic applications. We understand the origin of QI in terms of symmetry arguments, which show the robustness and generality of the effect. This also allows us to devise a concrete protocol for the electrostatic control of the spin polarization of the current by breaking the sublattice symmetry of graphene, by deposition on hexagonal boron nitride, paving the way to switchable spin filters. Such a system benefits from all of the extraordinary conduction properties of graphene, and at the same time, it does not require any external magnetic field to select the spin polarization, as magnetism emerges spontaneously at the edges of the nanoflake.

In this work we derive a general formula for the charge pumped in a superconducting nanocircuit. Our expression generalizes previous results in several ways, it is applicable both in the adiabatic and in the non-adiabatic regimes and it takes into account also the effect of an external environment. More specifically, by applying Floquet theory to Cooper pair pumping, we show that under a cyclic evolution the total charge transferred through the circuit is proportional to the derivative of the associated Floquet quasi-energy with respect to the superconducting phase difference. In the presence of an external environment the expression for the transferred charge acquires a transparent form in the Floquet representation. It is given by the weighted sum of the charge transferred in each Floquet state, the weights being the diagonal components of the stationary density matrix of the system expressed in the Floquet basis. In order to test the power of this formulation we apply it to the study of pumping in a Cooper pair sluice. We reproduce the known results in the adiabatic regime and we show new data in the non-adiabatic case.Comment: 9 page

Superconducting qubits coupled to electric or nanomechanical resonators display effects previously studied in quantum electrodynamics (QED) and extensions thereof. Here we study a driven qubit coupled to a low-frequency tank circuit with particular emphasis on the role of dissipation. When the qubit is driven to perform Rabi oscillations, with Rabi frequency in resonance with the oscillator, the latter can be driven far from equilibrium. Blue detuned driving leads to a population inversion in the qubit and lasing behavior of the oscillator ("single-atom laser"). For red detuning the qubit cools the oscillator. This behavior persists at the symmetry point where the qubit-oscillator coupling is quadratic and decoherence effects are minimized. Here the system realizes a "single-atom-twophoton laser". Φ Φ x (t) ac J J J M M C L U

Cooper pair pumping is a coherent process. We derive a general expression for the adiabatic pumped charge in superconducting nanocircuits in the presence of level degeneracy and relate it to non-Abelian holonomies of Wilczek and Zee. We discuss an experimental system where the non-Abelian structure of the adiabatic evolution manifests in the pumped charge.

Motivated by recent experiments, which demonstrated lasing and cooling of the electromagnetic modes in a resonator coupled to a superconducting qubit, we describe the specific mechanisms creating the population inversion, and we study the spectral properties of these systems in the lasing state. Different levels of the theoretical description, i.e., the semi-classical and the semi-quantum approximation, as well as an analysis based on the full Liouville equation are compared. We extend the usual quantum optics description to account for strong qubit-resonator coupling and include the effects of low-frequency noise. Beyond the lasing transition we find for a singleor few-qubit system the phase diffusion strength to grow with the coupling strength, which in turn deteriorates the lasing state.