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Investigation of Quantum Spin Squeezing in Quantum Information Theory.

نسرین هاشمی دیجوجین, قادر نجارباشی, بهمن سیفی

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

Coherent and squeezed photon states have attracted a lot attetion in long time ago, since these states can generate in laboratory. These states are satisfying in minimum uncertainty relation. In recently, states have generates with electrons by Bose-Einstein condensations and particles oscillations. Also,this states are satisfying in minimum uncertainty relation, with this difference that parameters in this states are the first and second moments of soin operators instead of position and momentum operators.The similarity phenomenon about squeezing photon is exist for spin with that distance. The source of spin squeezing in multi-qubit states is entanglement. One applecations of spin squeezing is to detect quantum entanglement which plays a key role in both the foundations of quantum physics and quantum computation processing. In recent years, spin squeezing stsate parameters have close relation with entanglement measure, concurrence, that we can characterize entanglement for a class of many-body spin- states. In reality, spin squeezing parameters are witnesse for many bode entanglement. In this paper; we study relation betweenspin squeezed states and entanglement. Then; we stuy the squeezing spin for -mode and -mode entangled coherent states.

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arXiv:1506.06906•Jun 23, 2015•1 citation
Coherent and squeezed photon states have attracted a lot attetion in long time ago, since these states can generate in laboratory. These states are satisfying in minimum uncertainty relation. In recently, states have generates with electrons by Bose-Einstein condensations and particles oscillations. Also,this states are satisfying in minimum uncertainty relation, with this difference that parameters in this states are the first and second moments of soin operators instead of position and momentum operators.The similarity phenomenon about squeezing photon is exist for spin with that distance. The source of spin squeezing in multi-qubit states is entanglement. One applecations of spin squeezing is to detect quantum entanglement which plays a key role in both the foundations of quantum physics and quantum computation processing. In recent years, spin squeezing stsate parameters have close relation with entanglement measure, concurrence, that we can characterize entanglement for a class of many-body spin- states. In reality, spin squeezing parameters are witnesse for many bode entanglement. In this paper; we study relation betweenspin squeezed states and entanglement. Then; we stuy the squeezing spin for -mode and -mode entangled coherent states.
This paper reviews quantum spin squeezing, which characterizes the sensitivity of a state with respect to SU(2) rotations, and is significant for both entanglement detection and high-precision metrology. We first present various definitions of spin squeezing parameters, explain their origin and properties for typical states, and then discuss spin-squeezed states produced with nonlinear twisting Hamiltonians. Afterwards, we explain pairwise correlations and entanglement in spin-squeezed states, as well as the relations between spin squeezing and quantum Fisher information, where the latter plays a central role in quantum metrology. We also review the applications of spin squeezing for detecting quantum chaos and quantum phase transitions, as well as the influence of decoherence on spin squeezing. Finally, we review several experimental realizations of spin squeezing, as well as their corresponding theoretical backgrounds, including: producing spin-squeezed states via particle collisions in Bose-Einstein condensates, transferring photon squeezing to atomic ensembles, and generating spin squeezing via quantum non-demolition measurements.
Entanglement witnesses based on first and second moments exist in the form of spin squeezing criteria for the detection of particle entanglement from collective measurements, and in the form of modified uncertainty relations for the detection of mode entanglement or steering. By revealing a correspondence between them, we show that metrologically useful spin squeezing reveals multimode entanglement in symmetric spin states that are distributed into addressable modes. We further derive tight state-independent multipartite entanglement bounds on the spin squeezing coefficient and point out their connection to widely used entanglement criteria that depend on the state's polarization. Our results are relevant for state-of-the-art experiments where symmetric entangled states are distributed into a number of addressable modes, such as split spin squeezed Bose-Einstein condensates.
Squeezed states, special kinds of entangled states, are known as a useful resource for quantum metrology. In interferometric sensors, they allow us to overcome the ‘classical’ projection noise limit stemming from the independent nature of the individual photons or atoms within the interferometer. Motivated by the potential impact on metrology as well as by fundamental questions in the context of entanglement, a lot of theoretical and experimental effort has been made to study squeezed states. The first squeezed states useful for quantum-enhanced metrology have been proposed and generated in quantum optics, where the squeezed variables are the coherences of the light field. In this tutorial, we focus on spin squeezing in atomic systems. We give an introduction to its concepts and discuss its generation in Bose–Einstein condensates. We discuss in detail the experimental requirements necessary for the generation and direct detection of coherent spin squeezing. Two exemplary experiments demonstrating adiabatically prepared spin squeezing based on motional degrees of freedom and diabatically realized spin squeezing based on internal hyperfine degrees of freedom are discussed.
Squeezed states, a special kind of entangled states, are known as a useful resource for quantum metrology. In interferometric sensors they allow to overcome the "classical" projection noise limit stemming from the independent nature of the individual photons or atoms within the interferometer. Motivated by the potential impact on metrology as wells as by fundamental questions in the context of entanglement, a lot of theoretical and experimental effort has been made to study squeezed states. The first squeezed states useful for quantum enhanced metrology have been proposed and generated in quantum optics, where the squeezed variables are the coherences of the light field. In this tutorial we focus on spin squeezing in atomic systems. We give an introduction to its concepts and discuss its generation in Bose-Einstein condensates. We discuss in detail the experimental requirements necessary for the generation and direct detection of coherent spin squeezing. Two exemplary experiments demonstrating adiabatically prepared spin squeezing based on motional degrees of freedom and diabatically realized spin squeezing based on internal hyperfine degrees of freedom are discussed.
Recent years have witnessed revolutionary improvement in the production, manipulation, characterization and quantification of multiatom (multiqubit) states - because of their promising applications in high precision atomic clocks, atomic interferrometry, quantum metrology and quantum information protocols. In the characterization and quantification of non-classical atomic correlations, two concepts namely, spin squeezing and quantum entanglement emerge. While spin squeezing originates from the uncertainty relation between atomic collective angular momentum operators, entanglement is a peculiar phenomena arising due to superpositions in the multiparticle Hilbert space. Here, we outline different quantitative measures of spin squeezing and discuss the intrinsic relation of spin squeezing with quantum entanglement in multiqubit systems.
These two accompanying papers treat two mode entanglement for systems of identical massive bosons and the relationship to spin squeezing and other quantum correlation effects. Entanglement is a key quantum feature of composite systems where the probabilities for joint measurements on the composite sub-systems are no longer determined from measurement probabilities on the separate sub-systems. We focus on the meaning of entanglement, the quantum paradoxes associated with entangled states, and important tests that allow an experimentalist to determine whether a quantum state - in particular, one for massive bosons is entangled. Our tests for entanglement fully utilise the symmetrisation principle and super-selection rules for bosonic massive particles. These papers provides detailed arguments necessary for the conclusions of a recent paper which presented results for rigorously demonstrating the entanglement of a two-mode Bose-Einstein condensate (BEC). In the first paper (I), we discuss the meaning of entanglement for systems of identical particles. For such systems, the relevant quantum density operators must satisfy the symmetrisation principle and global and local super-selection rules prohibiting states in which there are coherences between differing particle numbers. We fully justify these requirements. In the second quantisation approach, both the system and sub-systems are modes (or sets of modes) rather than particles, particles being associated with different mode occupancies. In the accompanying review paper (II), we consider spin squeezing and other tests for entanglement for two-mode bosonic systems. Starting from paper (I) we determine which tests are useful for detecting entanglement in massive bosonic (BEC), as opposed to photonic, systems. Several new inequalities are derived, and recent key experiments are analysed.