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Register a new userQuantum entanglement in coupled lossy waveguides using SU(2) and SU(1,1) Thermo-algebras
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Added by
Bindu Anubha Bambah
Publication date
2015
fields
Physics
and research's language is
English
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In this paper, the master equation for the coupled lossy waveguides is solved using the thermofield dynamics(TFD) formalism. This formalism allows the use of the underlying symmetry algebras SU(2) and SU(1,1), associated with the Hamiltonian of the coupled lossy waveguides,to compute entanglement and decoherence as a function of time for various input states such as NOON states and thermal states.
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The use of squeezing and entanglement allows advanced interferometers to detect signals that would otherwise be buried in quantum mechanical noise. High sensitivity instruments including magnetometers and gravitational wave detectors have shown enhanced signal-to-noise ratio (SNR) by injecting single-mode squeezed light into SU(2) interferometers, e.g. the Mach-Zehnder or Michelson topologies. The quantum enhancement in this approach is sensitive to losses, which break the fragile quantum correlations in the squeezed state. In contrast, SU(1,1) interferometers achieve quantum enhancement by noiseless amplification; they noiselessly increase the signal rather than reducing the quantum noise. Prior work on SU(1,1) interferometers has shown quantum-enhanced SNR11 and insensitivity to losses but to date has been limited to low powers and thus low SNR. Here we introduce a new interferometer topology, the SU(2)-in-SU(1,1) nested interferometer, that combines quantum enhancement, the high SNR possible with a SU(2) interferometer, and the loss tolerance of the SU(1,1) approach. We implement this interferometer using four-wave mixing in a hot atomic vapor and demonstrate 2:2(5) dB of quantum SNR enhancement, in a system with a phase variance nearly two orders of magnitude below that of any previous loss-tolerant enhancement scheme. The new interferometer enables new possibilities such as beyond-shot-noise sensing with wavelengths for which efficient detectors are not available.
A sufficient condition for a state |psi> to minimize the Robertson-Schr{o}dinger uncertainty relation for two observables A and B is obtained which for A with no discrete spectrum is also a necessary one. Such states, called generalized intelligent states (GIS), exhibit arbitrarily strong squeezing (after Eberly) of A and B. Systems of GIS for the SU(1,1) and SU(2) groups are constructed and discussed. It is shown that SU(1,1) GIS contain all the Perelomov coherent states (CS) and the Barut and Girardello CS while the Bloch CS are subset of SU(2) GIS.
In this communication we discuss SU(1,1)- and SU(2)-squeezing of an interacting system of radiation modes in a quadratic medium in the framework of Lie algebra. We show that regardless of which state being initially considered, squeezing can be periodically generated.
In this paper, we derive a general expression of the quantum Fisher information of an SU(1,1) interferometer with an arbitrary state and a Fock state as inputs by the phase-averaging method. Our results show that the same quantum Fisher information can be obtained regardless of the specific form of the arbitrary state. Then, we analytically prove that the parity measurement can saturate the quantum Cramer-Rao bound when the estimated phase sits at the optimal working point. For practical reasons, we investigate the phase sensitivity when the arbitrary state is a coherent or thermal state. We further show that a Fock state can indeed enhance the phase sensitivity within a constraint on the total mean photon number inside the interferometer.
The quantum stochastic phase estimation has many applications in the precise measurement of various physical parameters. Similar to the estimation of a constant phase, there is a standard quantum limit for stochastic phase estimation, which can be obtained with the Mach-Zehnder interferometer and coherent input state. Recently, it has been shown that the stochastic standard quantum limit can be surpassed with non-classical resources such as the squeezed light. However, practical methods to achieve the quantum enhancement in the stochastic phase estimation remains largely unexplored. Here we propose a method utilizing the SU(1,1) interferometer and coherent input states to estimate a stochastic optical phase. As an example, we investigate the Ornstein-Uhlenback stochastic phase. We analyze the performance of this method for three key estimation problems: prediction, tracking and smoothing. The results show significant reduction of the mean square error compared with the Mach-Zehnder interferometer under the same photon number flux inside the interferometers. In particular, we show that the method with the SU(1,1) interferometer can achieve the fundamental quantum scaling, the stochastic Heisenberg scaling, and surpass the precision of the canonical measurement.
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