QUANTUM STATE OF JOSEPHSON JUNCTION AS COOPER PAIR NUMBER-PHASE ENTANGLED STATE IN THE BOSONIC OPERATOR JOSEPHSON MODEL

2007 ◽  
Vol 21 (21) ◽  
pp. 3697-3706 ◽  
Author(s):  
HONG-YI FAN ◽  
JI-SUO WANG ◽  
XIANG-GUO MENG
Keyword(s):  
Josephson Junction ◽  
Quantum State ◽  
Cooper Pair ◽  
Geometric Distribution ◽  
Entangled State ◽  
Phase Operator ◽  
Schmidt Decomposition ◽  
Bosonic Operator ◽  
Pair Number

Based on Feynman's explanation about Cooper pair that "a bound pair acts as a Bose particle" and the bosonic operator Hamiltonian of the Josephson junction, we realize that the quantum state of the Josephson junction is a Cooper pair number-phase entangled state constructed by the phase operator across the junction. Its Schmidt decomposition is derived. The Cooper pair number-phase squeezed state's projection onto this entangled state leads to a geometric distribution.

COOPER-PAIR-NUMBER–PHASE SQUEEZING FOR THE BOSONIC HAMILTONIAN MODEL OF JOSEPHSON JUNCTION

2006 ◽  
Vol 20 (17) ◽  
pp. 1041-1047 ◽  
Author(s):  
HONG-YI FAN ◽  
JI-SUO WANG ◽  
YUE FAN
Keyword(s):  
Josephson Junction ◽  
Cooper Pair ◽  
Entangled State ◽  
Entangled State Representation ◽  
State Representation ◽  
Extra Energy ◽  
Bosonic Operator ◽  
Hamiltonian Model ◽  
Pair Number ◽  
Two Sides

Based on Feynman's explanation about the Cooper pair that "a bound pairs act as a Bose particle" and the bosonic operator Hamiltonian of Josephson junction (H.-Y. Fan, Int. J. Mod. Phys. B17 (2003) 2599) as well as the entangled state representation, we establish a possible number–phase squeezing mechanism for the Cooper-pair and the phase difference between the two sides of the junction. We find that when an extra energy (e.g. microwave radiation) is provided to the junction, then this squeezing mechanism can happen.

Phase State as a Cooper-Pair Number: Phase Minimum Uncertainty State for Josephson Junction

2003 ◽  
Vol 17 (13) ◽  
pp. 2599-2608 ◽  
Author(s):  
Hong-Yi Fan
Keyword(s):  
Josephson Junction ◽  
Cooper Pair ◽  
Uncertainty Relation ◽  
Phase State ◽  
Phase Operator ◽  
Operator Formalism ◽  
Hamiltonian Model ◽  
Pair Number ◽  
Minimum Uncertainty ◽  
Phase Uncertainty

Based on Feynman's explanation that a Cooper pair is "a bound pair act as a Bose particle", we propose a bosonic phase operator formalism and a bosonic Hamiltonian model for Josephson junction. The Cooper pair number — phase uncertainty relation is thus established. The corresponding minimum uncertainty state is derived which turns out to be a phase state.

OPERATOR JOSEPHSON EQUATION FOR A JOSEPHSON JUNCTION CONNECTED INTO A MESOSCOPIC LC CIRCUIT

2008 ◽  
Vol 22 (32) ◽  
pp. 3171-3177
Author(s):  
JI-SUO WANG ◽  
BAO-LONG LIANG ◽  
HONG-YI FAN
Keyword(s):  
Josephson Junction ◽  
Entangled State ◽  
Entangled State Representation ◽  
Phase Operator ◽  
State Representation ◽  
Modified Equations ◽  
Lc Circuit

We find that when a single Josephson junction is inserted into a mesoscopic LC circuit, the operator Josephson equation is modified accompanying with the modification of Farady equation describing the inductance. By virtue of the entangled state representation and using the appropriate phase operator in bosonic form we derive the modified equations.

ENTANGLED STATE REPRESENTATION FOR A PARTICLE ON A CIRCLE STUDIED IN TERMS OF BOSONIC OPERATOR REALIZATION OF ANGULAR MOMENTUM

2006 ◽  
Vol 21 (27) ◽  
pp. 2079-2085 ◽  
Author(s):  
HONG-YI FAN
Keyword(s):  
Quantum Mechanics ◽  
Angular Momentum ◽  
Entangled States ◽  
Entangled State ◽  
Entangled State Representation ◽  
Phase Operator ◽  
State Representation ◽  
New Formalism ◽  
Bosonic Operator ◽  
Operator Realization

By introducing the bosonic operator realization of angular momentum, we establish the entangled state representation for describing quantum mechanics of a particle on a circle. The phase operator, the angular momentum eigenstates, the lowering and ascending operators for angular momentum are all well expressed in the bosonic realization with the aid of appropriate entangled states, i.e. we establish a new formalism for the quantum mechanics of a particle on a circle.

Cooper-pair number–phase Wigner function for the bosonic operator Josephson model

2006 ◽  
Vol 359 (6) ◽  
pp. 580-586 ◽  
Author(s):  
Hong-Yi Fan ◽  
Ji-Suo Wang ◽  
Shu-guang Liu
Keyword(s):  
Wigner Function ◽  
Cooper Pair ◽  
Bosonic Operator ◽  
Pair Number

Assigning Values and States

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum State ◽  
Density Operator ◽  
Entangled State ◽  
Physical Situation ◽  
Born Rule ◽  
Correct Assignment ◽  
Significant Magnitude ◽  
Good Advice ◽  
Empirical Significance ◽  
Important Idea

If a quantum state is prescriptive then what state should an agent assign, what expectations does this justify, and what are the grounds for those expectations? I address these questions and introduce a third important idea—decoherence. A subsystem of a system assigned an entangled state may be assigned a mixed state represented by a density operator. Quantum state assignment is an objective matter, but the correct assignment must be relativized to the physical situation of an actual or hypothetical agent for whom its prescription offers good advice, since differently situated agents have access to different information. However this situation is described, it is true, empirically significant magnitude claims that make the description correct, while others provide the objective grounds for the agent’s expectations. Quantum models of environmental decoherence certify the empirical significance of these magnitude claims while also licensing application of the Born rule to others without mentioning measurement.

Entanglement

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Physical Condition ◽  
Physical System ◽  
Polarization State ◽  
Quantum Systems ◽  
Ghz State ◽  
Mathematical Representation ◽  
Entangled State ◽  
Physical Relation

Often a pair of quantum systems may be represented mathematically (by a vector) in a way each system alone cannot: the mathematical representation of the pair is said to be non-separable: Schrödinger called this feature of quantum theory entanglement. It would reflect a physical relation between a pair of systems only if a system’s mathematical representation were to describe its physical condition. Einstein and colleagues used an entangled state to argue that its quantum state does not completely describe the physical condition of a system to which it is assigned. A single physical system may be assigned a non-separable quantum state, as may a large number of systems, including electrons, photons, and ions. The GHZ state is an example of an entangled polarization state that may be assigned to three photons.

Time fractional evolution of a single quantum state and entangled state

2021 ◽  
Vol 147 ◽  
pp. 110930
Author(s):  
Chuanjin Zu ◽  
Yanming Gao ◽  
Xiangyang Yu
Keyword(s):  
Quantum State ◽  
Entangled State ◽  
Single Quantum
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