Mesoscopic multiply connected samples such as conducting rings, cylinders or tori exhibit quantum size phenomena originating from the Aharonov–Bohm effects. One of the most spectacular phenomena is a persistent current [1] which is a direct manifestation of quantum phase coherence of the current carriers over a mesoscopic length scale. At a non-zero temperature, T > 0, the phase coherence of carriers is weakened and the samples exhibit the dissipative Ohmic contribution to the total current. There is a regime of temperatures in which both phase-coherent and dissipative Ohmic currents coexist. Such currents generate a magnetic flux. Its properties can be studied via modelling based on kinetic equations like Langevin equations [2]. The long-time, steady states of the magnetic flux are characterized by properties of the stationary probability density obtained from the corresponding Langevin equation. For instance, if the stationary probability density is bimodal, i.e., it has two maxima it reflects the possibility of occurrence of non-zero magnetic fluxes and in consequence the currents. One can notice an obvious analogy to the Josephson-based flux qubits [3]. There are serious advantages for using non-superconducting samples like rings as a building blocks for qubit storage because due to a small size they seem to be more stable with respect to decoherence and dephasing [4]. For higher temperatures, when __________
Mesoscopic systems and the non-classical electromagnetic fields are of central importance for quantum information processing. Our aim is to present the significant impact of the non-classical radiation on the properties of persistent currents. We study mesoscopic rings or cylinders subject to both classical and non-classical magnetic flux. Our discussion is limited to oneand two-mode fields prepared in a given state. For the monochromatic radiation we study reduction of the current amplitude due to the quantum and classical noise in the field. We also present the change of the sign of the current from parato diamagnetic (and vice versa) controlled by the state of radiation. The effect of temperature will by shortly reviewed. There are two qualitatively distinct classes of two-mode fields: separable and entangled. This is reflected in the properties of the currents which become time-dependent for the fields in an entangled state. We investigate the effect of entanglement for the family of states with various amount of entanglement: from separable to Bell states quantified by the concurrence.
The quantum orbital motion of electrons in mesoscopic normal-metal rings threaded by a magnetic flux produces striking interference phenomena such as persistent currents due to the Aharonov-Bohm effect. Similarly, when a quantum spin adiabatically follows a magnetic field that rotates slowly in time, the phase of its state vector acquires an additional contribution known as the Berry phase. We explore the combination of these two quantum phenomena by examining the interplay between orbital and spin degrees of freedom for a charged spin-1/2 particle moving in a mesoscopic ring embedded in a classical, static inhomogeneous magnetic field, i.e, a texture. As a consequence of its orbital motion through the texture, the spin experiences, via the Zeeman interaction, a varying magnetic field. This results in a Berry---or geometric---phase, leading to persistent (i.e., equilibrium) currents of charge and spin. These mesoscopic phenomena are related to (but should be distinguished from) the conventional persistent currents that result from magnetic flux through a ring. We develop a path-integral approach to decouple the orbital and spin motion and, by using an adiabatic approximation, we compute the equilibrium expectation values of the persistent charge and spin currents and the magnetization. We find that the persistent currents depend on the texture in a striking manner through a geometric phase (related to a surface area characterizing the texture) and a geometric vector (related to the projections of this area). In the special case of a cylindrically symmetric texture we use a spectrum obtained by Kuratsuji and Iida to obtain exact results that confirm, independently, the validity of the path-integral approach in the adiabatic limit. We discuss the connection between the geometric vector and quantum-mechanical correlations, and examine quantum fluctuations and the zero-point energy.
The possibility of making a flux qubit on a nonsuperconducting mesoscopic ballistic quasi-one-dimensional ring is discussed. We showed that such a ring can be effectively reduced to a two-state system with two external control parameters. The two states carry opposite persistent currents and are coupled by tunneling, which leads to a quantum superposition of states. The qubit states can be manipulated by resonant microwave pulses. The flux state of the sample can be measured by a superconducting quantum interference device magnetometer. Two or more qubits can be coupled by the flux the circulating currents generate. The problem of decoherence is also discussed.
We perform analytical calculations to study the persistent current I of a q-charged hard-core boson gas in mesoscopic rings enclosing a magnetic flux \ensuremath{\Phi}, and find that this current is periodic in \ensuremath{\Phi} with the period ${\mathrm{\ensuremath{\Phi}}}_{0}$=hc/q. More interestingly, in the presence of a single \ensuremath{\delta}-function impurity, it has been found that there generally exists a spontaneous Aharonov-Bohm flux as long as the current-induced flux is included.
We study quantum phase-slip (QPS) processes in a superconducting ring containing
N Josephson junctions and threaded by an external static magnetic flux ${\ensuremath{\Phi}}_{B}$. In such a system, a QPS consists of a quantum tunneling event connecting two distinct classical states of the phases with different persistent currents [Matveev et al., Phys. Rev. Lett. 89, 096802 (2002)]. When the Josephson coupling energy
EJ of the junctions is larger than the charging energy
EC=e2/2C, where
C is the junction capacitance, the quantum amplitude for the QPS process is exponentially small in the ratio
EJ/EC. At given magnetic flux, each QPS can be described as the tunneling of the phase difference of a single junction of almost $2\ensuremath{\pi}$, accompanied by a small harmonic displacement of the phase difference of the other $N\ensuremath{-}1$ junctions. As a consequence, the total QPS amplitude ${\ensuremath{\nu}}_{\mathrm{ring}}$ is a global property of the ring. Here, we study the dependence of ${\ensuremath{\nu}}_{\mathrm{ring}}$ on the ring size
N, taking into account the effect of a finite capacitance
C0 to ground, which leads to the appearance of low-frequency dispersive modes. Josephson and charging effects compete and lead to a nonmonotonic dependence of the ring's critical current on
N. For $N\ensuremath{\rightarrow}\ensuremath{\infty}$, the system converges either towards a superconducting or an insulating state, depending on the ratio between the charging energy
E0=e2/2C0 and the Josephson coupling energy
EJ.