COHERENT EVOLUTION AND TUNNELING CHARGE STEP IN A DRIVEN MESOSCOPIC JOSEPHSON JUNCTION

1999 ◽  
Vol 13 (12n13) ◽  
pp. 391-397
Author(s):  
BIN SHAO ◽  
JIAN ZOU ◽  
QIANSHU LI
Keyword(s):  
Josephson Junction ◽  
Coherent States ◽  
Evolution Operator ◽  
Weak Link ◽  
Vacuum State ◽  
Time Dependent ◽  
Unitary Evolution ◽  
Dc Voltage ◽  
Mesoscopic System ◽  
Charge Tunneling

We consider a circular superconductor with a weak link mesoscopic Josephson junction in the presence of a dc voltage bias. Using the time-dependent perturbated method, we obtain the unitary evolution operator of the mesoscopic junction system and show that an initial vacuum state of the junction can evolve into a class of superposition of coherent states. Further, we show that the charge tunneling through the junction can exhibit step properties in the mesoscopic system.

scholarly journals Specifying the Unitary Evolution of a Qudit for a General Nonstationary Hamiltonian via the Generalized Gell-Mann Representation

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 521
Author(s):  
Elena R. Loubenets ◽  
Christian Käding
Keyword(s):  
Vector Space ◽  
Wide Class ◽  
Analytical Study ◽  
Evolution Operator ◽  
Unit Vector ◽  
Time Dependent ◽  
Unitary Evolution ◽  
Analytical Expression ◽  
Optimal Realizations ◽  
Quantum Technology

Optimal realizations of quantum technology tasks lead to the necessity of a detailed analytical study of the behavior of a d-level quantum system (qudit) under a time-dependent Hamiltonian. In the present article, we introduce a new general formalism describing the unitary evolution of a qudit ( d ≥ 2 ) in terms of the Bloch-like vector space and specify how, in a general case, this formalism is related to finding time-dependent parameters in the exponential representation of the evolution operator under an arbitrary time-dependent Hamiltonian. Applying this new general formalism to a qubit case ( d = 2 ) , we specify the unitary evolution of a qubit via the evolution of a unit vector in R 4 , and this allows us to derive the precise analytical expression of the qubit unitary evolution operator for a wide class of nonstationary Hamiltonians. This new analytical expression includes the qubit solutions known in the literature only as particular cases.

QUANTUM FLUCTUATION AND REVIVAL OF SUPERCURRENT IN MESOSCOPIC JOSEPHSON JUNCTION DRIVEN BY CLASSICAL PERIODIC FIELD

2000 ◽  
Vol 14 (01) ◽  
pp. 29-40
Author(s):  
QIANSHU LI ◽  
BIN SHAO ◽  
JIAN ZOU ◽  
RONGYAO WANG
Keyword(s):  
Magnetic Field ◽  
Josephson Junction ◽  
Time Evolution ◽  
Coherent States ◽  
Quantum Fluctuation ◽  
Vacuum State ◽  
Classical Field ◽  
Superposition State ◽  
Periodic Field ◽  
Sinusoidal Magnetic Field

We examine an effective bosonic Hamiltonian describing a mesoscopic Josephson junction driven by a sinusoidal magnetic field. We study the effects caused by the Josephson nonlinearity and find that an initial vacuum state of the junction can evolve into a class of superposition state of coherent states. Further, we investigate the reduced quantum fluctuation of the junction variables and the dynamics of the supercurrent. Our results show that, due to the effect of Josephson nonlinearity, the time evolution of the supercurrent can exhibit the collapse and revival even when the junction is driven by a classical field.

Creating Coherent States in a Mesoscopic Josephson Junction

1998 ◽  
Vol 12 (25n26) ◽  
pp. 1069-1074
Author(s):  
Shao Bin ◽  
Jian Zou ◽  
Qianshu Li
Keyword(s):  
Schrödinger Equation ◽  
Coherent State ◽  
Josephson Junction ◽  
Ground State ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Hamiltonian Operator ◽  
Classical Field ◽  
The State ◽  
Time Dependent

We examine a system of mesoscopic Josephson junction driven by classical field and solve the time-dependent Schrödinger equation of the system with the help of the time-dependent invariant of the Hamiltonian operator. We show that the state of the system can evolve a pure coherent state when the junction is prepared initially in its ground state.

scholarly journals Large Time Decay of Solutions to a Linear Nonautonomous System in Exterior Domains

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 841
Author(s):  
Toshiaki Hishida
Keyword(s):  
Evolution Operator ◽  
Large Time ◽  
Rigid Motion ◽  
Time Dependent ◽  
Energy Relation ◽  
Exterior Domains ◽  
Decay Properties ◽  
Decay Of Solutions ◽  
Whole Space ◽  
Expository Paper

In this expository paper, we study Lq-Lr decay estimates of the evolution operator generated by a perturbed Stokes system in n-dimensional exterior domains when the coefficients are time-dependent and can be unbounded at spatial infinity. By following the approach developed by the present author for the physically relevant case where the rigid motion of the obstacle is time-dependent, we clarify that some decay properties of solutions to the same system in whole space Rn together with the energy relation imply the desired estimates in exterior domains provided n≥3.

INTERACTION OF MESOSCOPIC JOSEPHSON JUNCTION WITH A SUCCESSIVE SQUEEZED COHERENT FIELD

2000 ◽  
Vol 14 (16) ◽  
pp. 609-618
Author(s):  
V. A. POPESCU
Keyword(s):  
Coherent State ◽  
Josephson Junction ◽  
Coherent States ◽  
Quantum Noise ◽  
Shapiro Steps ◽  
Superconducting Ring ◽  
Coherent Field ◽  
Current Voltage ◽  
Quantum Current ◽  
The Difference

Signal-to-quantum noise ratio for quantum current in mesoscopic Josephson junction of a circular superconducting ring can be improved if the electromagnetic field is in a successive squeezed coherent state. The mesoscopic Josephson junctions can feel the difference between the successive squeezed coherent states and other types of squeezed coherent states because their current–voltage Shapiro steps are different. We compare our method with another procedure for superposition of two squeezed coherent states (a squeezed even coherent state) and consider the effect of different large inductances on the supercurrent.

scholarly journals CANONICAL FORM OF THE EVOLUTION OPERATOR OF A TIME-DEPENDENT HAMILTONIAN IN THE THREE LEVEL SYSTEM

2011 ◽  
Vol 08 (03) ◽  
pp. 647-655
Author(s):  
KAZUYUKI FUJII
Keyword(s):  
Differential Equations ◽  
Canonical Form ◽  
Evolution Operator ◽  
Time Dependent ◽  
Level System ◽  
Riccati Differential Equations

In this paper we study the evolution operator of a time-dependent Hamiltonian in the three level system. The evolution operator is based on SU(3) and its dimension is eight, so we obtain three complex Riccati differential equations interacting with one another (which have been obtained by Fujii and Oike) and two real phase equations. This is a canonical form of the evolution operator.

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