Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

John Wiley & Sons, Inc. eBooks

Quantum-Optical States in Finite-Dimensional Hilbert Space. II. State Generation

W. Leoński, Adam Miranowicz

Published Apr 2, 2003• 38 citations
Publisher

Abstract

The authors begin by summarizing some schemes of generating finite-dimensional (FD) quantum-optical states. Although it is possible to generate n-photon Fock states and then to construct a desired state from these states, the focus of the chapter is on generation schemes that lead directly to the FD coherent states and FD squeezed vacuum. The method described is based on the quantum nonlinear oscillator evolution. The oscillator is assumed to be driven by external excitation. Depending on the character of the excitation, various FD states can be produced.

DOI
10.1002/0471231479.ch4

Related papers

Quantum-Optical States in Finite-Dimensional Hilbert Space. I. General Formalism

Adam Miranowicz, W. Leoński, Nobuyuki Imoto

This chapter presents two essentially different constructions of harmonic oscillator states in a finite-dimensional (FD) Hilbert space. The authors propose some new definitions of the states and find their explicit forms in the Fock representation. For the convenience of the reader, they bring together several known FD quantum-optical states, including FD coherent states, FD phase coherent states, FD displaced number states, FD Schrödinger cats, and FD squeezed vacuums. The discrete Wigner function is applied in order to demonstrate intriguing properties of the various states.

arXiv:quant-ph/0108080•John Wiley & Sons, Inc. eBooks•Apr 2, 2003•37 citations

Finite-dimensional coherent-state generation and quantum-optical nonlinear oscillator models

W. Leon-acuteski

We discuss a system comprising a cavity with a nonlinear medium of k-order and an external coherent field excitation. We assume that the cavity field was initially in vacuum state. We show that for the case of weak external field our system behaves similarly to one described in finite-dimensional Hilbert space. Moreover, we perform numerical calculations simulating the dynamics of our system and compare the results with those of analytical attempts.

Physical Review A•May 1, 1997•47 citations

FINITE-DIMENSIONAL SQUEEZED VACUUM AND ITS GENERATION 1

Adam Miranowicz

A squeezed vacuum in a finite-dimensional Hilbert space (FDHS) is defined. Its explicit Fock expansion is found. We show that our state goes over into the standard squeezed vacuum if the squeeze parameter squared is much less than the dimension of FDHS. A method to generate finite-dimensional squeezed vacuum is proposed. 1

•Jan 1, 1998•1 citation

Finite-dimensional states and entanglement generation

Doan Quoc Khoa

We studied a system that has two nonlinear oscillators with different frequencies. These oscillators are coupled via a nonlinear interaction. With the aim of excite the system, we used two external coherent fields. It follows from numerical simulation that evolution of the system which is likely to be a combination of Fock states. THerefore, the deliberated system behaves as so-called nonlinear quantum scissor. However, evolution of the system generates Bell-like states in some times with exact high probability. The system creates a truncation of optical states, which leads to obtain two-qubit states due to the nonlinear properties of oscillators and their interaction.

•Jan 1, 2018•0 citations

Quantum-optical states in finite-dimensional Hilbert space. II. State generation

W. Leoński, Adam Miranowicz

In the second part of our review (for the first part see quant-ph/0108080), we discuss a physical model for generation of "truncated" coherent and squeezed states in finite-dimensional Hibert spaces.

arXiv:quant-ph/0110146•Oct 25, 2001•5 citations

Linear optical extraction of photon-number Fock states from coherent states

Kaoru Sanaka

Photon-number Fock states play important roles in quantum optics. However, the generation of the states are very difficult because of the lack of large effective nonlinearities. In this Rapid Communication, I show a scheme to produce the Fock state from an input coherent state by using only linear optics method and projection measurements. I analyze the case of five-photon number state generation from coherent states for a specific case of the scheme. It is possible to remove the vacuum state from the output state when one introduces quantum nondemolition measurement that can also be implemented with all linear optics setup.

Physical Review A•Feb 4, 2005•29 citations
The authors begin by summarizing some schemes of generating finite-dimensional (FD) quantum-optical states. Although it is possible to generate n-photon Fock states and then to construct a desired state from these states, the focus of the chapter is on generation schemes that lead directly to the FD coherent states and FD squeezed vacuum. The method described is based on the quantum nonlinear oscillator evolution. The oscillator is assumed to be driven by external excitation. Depending on the character of the excitation, various FD states can be produced.
This chapter presents two essentially different constructions of harmonic oscillator states in a finite-dimensional (FD) Hilbert space. The authors propose some new definitions of the states and find their explicit forms in the Fock representation. For the convenience of the reader, they bring together several known FD quantum-optical states, including FD coherent states, FD phase coherent states, FD displaced number states, FD Schrödinger cats, and FD squeezed vacuums. The discrete Wigner function is applied in order to demonstrate intriguing properties of the various states.
We studied a system that has two nonlinear oscillators with different frequencies. These oscillators are coupled via a nonlinear interaction. With the aim of excite the system, we used two external coherent fields. It follows from numerical simulation that evolution of the system which is likely to be a combination of Fock states. THerefore, the deliberated system behaves as so-called nonlinear quantum scissor. However, evolution of the system generates Bell-like states in some times with exact high probability. The system creates a truncation of optical states, which leads to obtain two-qubit states due to the nonlinear properties of oscillators and their interaction.
Photon-number Fock states play important roles in quantum optics. However, the generation of the states are very difficult because of the lack of large effective nonlinearities. In this Rapid Communication, I show a scheme to produce the Fock state from an input coherent state by using only linear optics method and projection measurements. I analyze the case of five-photon number state generation from coherent states for a specific case of the scheme. It is possible to remove the vacuum state from the output state when one introduces quantum nondemolition measurement that can also be implemented with all linear optics setup.