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arXiv:0812.0507 · Physical Review A

Conditional preparation of arbitrary superpositions of atomic Dicke states

Karel Lemr, Jaromı́r Fiurášek

Published Apr 9, 2009• 12 citations
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Abstract

We propose an experimentally accessible procedure for conditional preparation of highly nonclassical states of collective spin of an atomic ensemble. The quantum state engineering is based on a combination of quantum nondemolition interaction between atoms and light previously prepared in a non-Gaussian state using photon subtraction from squeezed vacuum beam, homodyne detection on the output light beam, and a coherent displacement of atomic state. The procedure is capable of nondeterministic preparation of a wide class of superpositions of atomic Dicke states. We present several techniques to optimize the performance of the protocol and maximize the trade off between fidelity of prepared state and success probability of the scheme.

DOI
10.1103/physreva.79.043808

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We propose an experimentally accessible procedure for conditional preparation of highly nonclassical states of collective spin of an atomic ensemble. The quantum state engineering is based on a combination of quantum nondemolition interaction between atoms and light previously prepared in a non-Gaussian state using photon subtraction from squeezed vacuum beam, homodyne detection on the output light beam, and a coherent displacement of atomic state. The procedure is capable of nondeterministic preparation of a wide class of superpositions of atomic Dicke states. We present several techniques to optimize the performance of the protocol and maximize the trade off between fidelity of prepared state and success probability of the scheme.
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We present a protocol for generating nonclassical states of atomic spin ensembles through the backaction induced by a hybrid measurement of light that is entangled with atoms, combining both homodyne and single-photon detection. In phase I of the protocol we create a spin-squeezed state by measuring the light's polarization rotation due to the Faraday effect in a balanced polarimeter, equivalent to a homodyne measurement. In phase II we send a second probe beam through the sample and detect single photons scattered into the signal mode. Before doing so, we rotate the uncertainty bubble to increase the projection fluctuations of the measured spin component. This increases the coupling strength between the atoms and photons and thus the rate of scattering of single photons into the signal mode. In the ideal case, the result is a squeezed Dicke state, with substantial quantum advantage for sensing spin rotations. We benchmark the protocol's utility in the presence of inevitable decoherence due to optical pumping using the Fisher information as a measure of quantum advantage. We show that in the presence of decoherence, the quantum Fisher information associated with the non-Gaussian mixed state we prepare is substantially larger than the classical Fisher information obtained from the standard measurement of spin rotations. We deduce a measurement basis that is close to optimal for achieving the quantum Cram\'er-Rao bound in the presence of decoherence.
We investigate an optical scheme to conditionally engineer quantum states using a beam splitter, homodyne detection, and a squeezed vacuum as an ancillar state. This scheme is efficient in producing non-Gaussian quantum states such as squeezed single photons and superpositions of coherent states (SCSs). We show that a SCS with well defined parity and high fidelity can be generated from a Fock state of $n\ensuremath{\leqslant}4$, and conjecture that this can be generalized for an arbitrary nnn Fock state. We describe our experimental demonstration of this scheme using coherent input states and measuring experimental fidelities that are only achievable using quantum resources.
Nonclassical-state generation is an important component throughout experimental quantum science for quantum information applications and probing the fundamentals of physics. Here, we investigate permutations of quantum nondemolition quadrature measurements and single quanta addition or subtraction to prepare quantum superposition states in bosonic systems. The performance of each permutation is quantified and compared using several different nonclassicality criteria including Wigner negativity, nonclassical depth, and optimal fidelity with a coherent-state superposition. We also compare the performance of our protocol using squeezing instead of a quadrature measurement and find that the purification provided by the quadrature measurement can significantly increase the nonclassicality generated. Our approach is ideally suited for implementation in light-matter systems such as quantum optomechanics and atomic spin ensembles, and offers considerable robustness to initial thermal occupation.