By Using Number State Filtered Coherent States to Improve Phase Sensitivity with Multiple Passes

Uncertainty relations for the time-dependent singular oscillator in the number state and in the coherent state are investigated. We applied our developement to the Caldirola–Kanai oscillator perturbed by a singularity. For this system, the variation (Δx) decreased exponentially while (Δp) increased exponentially with time both in the number and in the coherent states. As k → 0 and χ → 0, the number state uncertainty relation in the ground state becomes 0.583216ℏ which is somewhat larger than that of the standard harmonic oscillator, ℏ/2. On the other hand, the uncertainty relation in all excited states become smaller than that of the standard harmonic oscillator with the same quantum number n. However, as k → ∞ and χ → 0, the uncertainty relations of the system approach the uncertainty relations of the standard harmonic oscillator, (n+1/2)ℏ.

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Phase sensitivity of an $\operatorname{SU}(1,1)$ interferometer via product detection

EPJ Quantum Technology ◽

10.1140/epjqt/s40507-021-00110-1 ◽

2021 ◽

Vol 8 (1) ◽

Author(s):

Qingle Wang ◽

Yami Fang ◽

Xiaoping Ma ◽

Dong Li

Keyword(s):

Coherent States ◽

The Other ◽

Phase Sensitivity ◽

Homodyne Detection ◽

Quantum Metrology ◽

Parametric Amplifiers ◽

Detection Scheme ◽

Beam Splitters ◽

Cramer Rao Bound

AbstractWe theoretically analyze the phase sensitivity of an $\operatorname{SU}(1,1)$ SU ( 1 , 1 ) interferometer with various input states by product detection in this paper. This interferometer consists of two parametric amplifiers that play the role of beam splitters in a traditional Mach–Zehnder interferometer. The product of the amplitude quadrature of one output mode and the momentum quadrature of the other output mode is measured via balanced homodyne detection. We show that product detection has the same phase sensitivity as parity detection for most cases, and it is even better in the case with two coherent states at the input ports. The phase sensitivity is also compared with the Heisenberg limit and the quantum Cramér–Rao bound of the $\operatorname{SU}(1,1)$ SU ( 1 , 1 ) interferometer. This detection scheme can be easily implemented with current homodyne technology, which makes it highly feasible. It can be widely applied in the field of quantum metrology.

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THE DEPENDENCY ON THE SQUEEZING PARAMETER FOR THE UNCERTAINTY RELATION IN THE SQUEEZED STATES OF THE TIME-DEPENDENT OSCILLATOR

International Journal of Modern Physics B ◽

10.1142/s0217979204026135 ◽

2004 ◽

Vol 18 (16) ◽

pp. 2307-2324 ◽

Cited By ~ 5

Author(s):

JEONG RYEOL CHOI

Keyword(s):

Quantum Mechanics ◽

Coherent State ◽

Coherent States ◽

Uncertainty Relation ◽

Time Dependent ◽

Squeezed States ◽

Time Dependency ◽

Minimum Value ◽

Number State

We obtained the uncertainty relation in squeezed states for a time-dependent oscillator. The uncertainty relation in coherent states is same as that of the number states with n=0. However, the uncertainty relation in squeezed states does not satisfy this property and depends on squeezing parameter c. For instance, the uncertainty relation is ℏ/2 which is the minimum value as far as quantum mechanics permits for c=1, same as that in coherent state for c=±∞, and infinity for c=-1. If the time-dependency of the Hamiltonian for the system vanishes, the uncertainty relation in squeezed states will no longer depend on c and becomes the same as that in number state with n=0, like the uncertainty relation in coherent states.

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Number state filtered coherent states

Quantum Information Processing ◽

10.1007/s11128-018-1995-6 ◽

2018 ◽

Vol 17 (9) ◽

Cited By ~ 8

Author(s):

Nilakantha Meher ◽

S. Sivakumar

Keyword(s):

Coherent States ◽

Number State

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Wigner function and phase sensitivity of photon-added coherent states and number states as inputs of MZI

Optik ◽

10.1016/j.ijleo.2020.165013 ◽

2020 ◽

Vol 220 ◽

pp. 165013

Author(s):

Chao-Ping Wei ◽

Li-Yun Hu

Keyword(s):

Wigner Function ◽

Coherent States ◽

Phase Sensitivity

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EVEN AND ODD DISPLACED NUMBER STATE

Modern Physics Letters B ◽

10.1142/s021798490500916x ◽

2005 ◽

Vol 19 (26) ◽

pp. 1347-1360 ◽

Cited By ~ 1

Author(s):

GUILHERME C. DE OLIVEIRA ◽

PAULO S. MELO ◽

CELIA M. A. DANTAS ◽

ELIAS DE S. LEITE

Keyword(s):

Phase Difference ◽

Coherent States ◽

Statistical Properties ◽

Level Atom ◽

Number State

In this paper we will study the statistical properties of a generalized superposition of two displaced number states of the form, [Formula: see text] with a phase difference of φ between them. A particular case of this state is obtained when we consider n1=n2=n and α1=-α2=α, which we will call even and odd displaced number state. It will be shown that they are the generalization of the even and odd coherent states. The generation of this states, based on the dispersive interaction with a two-level atom, will also be discussed.

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