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arXiv:0805.2910

Collective States and Symmetric Local Decoherence in Large Ensembles of Qubits

Bradley A. Chase, J. M. Geremia

Published May 19, 2008• 0 citations
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Abstract

The symmetric collective states of an atomic spin ensemble (i.e., many-body states that are invariant under particle exchange) are not preserved by decoherence that acts identically but individually on members of the ensemble. We develop a class of collective states in an ensemble of N spin-1/2 particles that is invariant under symmetric local decoherence and find that the dimension of the Hilbert space spanned by these collective states scales only as N^2. We then investigate the open system dynamics of experimentally relevant non-classical collective atomic states, including Schroedinger cat and spin squeezed states, subject to various symmetric but local decoherence models.

DOI
10.48550/arxiv.0805.2910

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The symmetric collective states of an atomic spin ensemble (i.e., many-body states that are invariant under particle exchange) are not preserved by decoherence that acts identically but individually on members of the ensemble. We develop a class of collective states in an ensemble of N spin-1/2 particles that is invariant under symmetric local decoherence and find that the dimension of the Hilbert space spanned by these collective states scales only as N^2. We then investigate the open system dynamics of experimentally relevant non-classical collective atomic states, including Schroedinger cat and spin squeezed states, subject to various symmetric but local decoherence models.
When the dynamics of a spin ensemble are expressible solely in terms of symmetric processes and collective spin operators, the symmetric collective states of the ensemble are preserved. These many-body states, which are invariant under particle relabeling, can be efficiently simulated since they span a subspace whose dimension is linear in the number of spins. However, many open system dynamics break this symmetry, most notably when ensemble members undergo identical, but local, decoherence. In this paper, we extend the definition of symmetric collective states of an ensemble of spin-1∕21∕21∕2 particles in order to efficiently describe these more general collective processes. The corresponding collective states span a subspace that grows quadratically with the number of spins. We also derive explicit formulas for expressing arbitrary, identical, local decoherence in terms of these states. We then investigate the open system dynamics of experimentally relevant nonclassical collective atomic states, including superposition and spin squeezed states, subject to various symmetric but local decoherence models.
It has become common practice to model large spin ensembles as an effective pseudospin with total angular momentum J=NjJ=\mathit{Nj}J=Nj, where jjj is the spin per particle. Such approaches (at least implicitly) restrict the quantum state of the ensemble to the so-called symmetric Hilbert space. Here, we argue that symmetric states are not generally well preserved under the type of decoherence typical of experiments involving large clouds of atoms or ions. In particular, symmetric states are rapidly degraded under models of decoherence that act identically but locally on the different members of the ensemble. Using an approach [Phys. Rev. A 78, 052101 (2008)] that is not limited to the symmetric Hilbert space, we explore potential pitfalls in the design and interpretation of experiments on spin-squeezing and collective atomic phenomena when the properties of the symmetric states are extended to systems where they do not apply.
We investigate the decoherence of a superposition of symmetric collective internal states of an atomic ensemble due to inhomogeneous coupling to external control fields. For asymptotically large system, we find N\sqrt{N}N​ as the characteristic decoherence rate scale with N being the total number of atoms. Our results shed new light on attempts for realizing quantum information processing and storage with atomic ensembles.
The influence of decoherence on quantum memories for photons based on atomic ensembles is discussed. It is shown that despite the large entanglement of the collective storage states, corresponding to single photons or nonclassical states of light, the sensitivity to decoherence does not scale with the number of atoms. This is due to the existence of equivalence classes of storage states, which have the same projection onto the relevant quasiparticle mode (dark-state polariton). Several decoherence processes resulting from uncorrelated individual reservoir couplings are analyzed in detail: single-atom spin flips and dephasing, atom loss, and motion of atoms. Furthermore, it is shown that the sensitivity to collective decoherence processes that affect all polariton modes with comparable strength does also not increase with the number of atoms.
Quantum entanglement reflects itself through non-local correlations among the subsystems of a quantum system. This thesis focuses on constructing a complete set of local invariants characterizing symmetric two qubit systems and analyzing the pairwise entanglement properties like collective spin squeezing - exhibited by multiqubits - in terms of two qubit entanglement invariants. Further, the collective pairwise entanglement properties of symmetric multiqubit states are shown to be captured entirely by the off diagonal block of the covariance matrix.
The scalable production of multipartite entangled states in ensembles of qubits is a crucial function of quantum devices, as such states are an essential resource both for fundamental studies on entanglement, as well as for applied tasks. Here we focus on the U(1) symmetric Hamiltonians for qubits with dipolar interactions-a model realized in several state-of-the-art quantum simulation platforms for lattice spin models, including Rydberg-atom arrays with resonant interactions. Making use of exact and variational simulations, we theoretically show that the nonequilibrium dynamics generated by this Hamiltonian shares fundamental features with that of the one-axis-twisting model, namely, the simplest interacting collective-spin model with U(1) symmetry. The evolution governed by the dipolar Hamiltonian generates a cascade of multipartite entangled states-spin-squeezed states, Schrödinger's cat states, and multicomponent superpositions of coherent spin states. Investigating systems with up to N=144 qubits, we observe full scalability of the entanglement features of these states directly related to metrology, namely, scalable spin squeezing at an evolution time O(N^{1/3}) and Heisenberg scaling of sensitivity of the spin parity to global rotations for cat states reached at times O(N). Our results suggest that the native Hamiltonian dynamics of state-of-the-art quantum simulation platforms, such as Rydberg-atom arrays, can act as a robust source of multipartite entanglement.