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Journal of Physics B Atomic Molecular and Optical Physics

Optimization of the environment for generating entanglement and spin squeezing

Da Yang Tan, Adam Zaman Chaudhry, Jiangbin Gong

Published Apr 17, 2015• 4 citations
Publisher

Abstract

Abstract We study the concurrence of two qubits and spin squeezing of N qubits interacting with a common environment using an exactly solvable pure dephasing model. We show that the concurrence and spin squeezing generated via the interaction with the common environment depends on the properties of the environment. Consequently, we optimize over the environmental properties, and in particular the Ohmicity parameter, in order to achieve the maximal quantum resource generation. We also show that there is a weak dependence between the maximum concurrence and the temperature, allowing the results to be experimentally realized in a realistic temperature regime.

DOI
10.1088/0953-4075/48/11/115505

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Abstract We study the concurrence of two qubits and spin squeezing of N qubits interacting with a common environment using an exactly solvable pure dephasing model. We show that the concurrence and spin squeezing generated via the interaction with the common environment depends on the properties of the environment. Consequently, we optimize over the environmental properties, and in particular the Ohmicity parameter, in order to achieve the maximal quantum resource generation. We also show that there is a weak dependence between the maximum concurrence and the temperature, allowing the results to be experimentally realized in a realistic temperature regime.
We study entanglement generated between a qubit and a super-ohmic bosonic bath due to their joint evolution which leads to pure dephasing of the qubit. We tune the parameters of the interaction, so that the decoherence is quantitatively independent of the number of bosonic modes taken into account (and corresponds to realistic decoherence seen in small excitonic quantum dots coupled to an environment of phonons) and investigate, how the entanglement generated depends on the size of the environment. A second parameter of interest is the mixedness of the initial state of the environment which is controlled by temperature. We show analytically that for a pure initial state of the environment (zero temperature here), entanglement does not depend on environment size. At finite temperatures (mixed initial state of the environment), the generated entanglement decreases with the increase of environment size. This effect is stronger for larger temperatures, when the environment is initially more mixed, but in the limit of an infinitely large environment, no entanglement is created at any finite temperature.
Using an exactly solvable pure dephasing model, we show how entanglement between qubits can be generated via the interaction with a common environment and concurrent application of suitable control pulses. The control pulses are able to effectively remove the detrimental effect of the environment while preserving the indirect interaction between the qubits, thereby leading to the generation of near-perfect entanglement. Furthermore, we also investigate the entanglement dynamics if the qubits are directly interacting; this interaction may even contain a noise term. The present of this additional noise leads to an additional decoherence term. This decoherence term cannot be removed by applying the pulses at the same time to both qubits. Rather, we show that by introducing a time delay between the two pulse sequences, near-perfect entanglement can still be generated via the interaction with the common environment.
We propose a straightforward experimental protocol to test whether qubit-environment entanglement is generated during pure dephasing of a qubit. The protocol is implemented using only measurements and operations on the qubit---it does not involve the measurement of the system-environment state of interest, but the preparation and measurement of the qubit in two simple variations. A difference in the time dependencies of qubit coherence between the two cases testifies to the presence of entanglement in the state of interest. Furthermore, it signifies that the environment-induced noise experienced by the qubit cannot be modeled as a classical stochastic process independent of the qubit state. We demonstrate the operation of this protocol on a realistically modeled nitrogen-vacancy center spin qubit in diamond interacting with a nuclear spin environment, and show that the generation of entanglement should be easily observable in this case.
Spin squeezing, a compelling manifestation of multiparticle entanglement, is considered one of the most promising quantum resources. Non-Markovian characteristics play a crucial role in many critical physical processes involving strong system-environment interactions. We investigate the generation of spin squeezing in a hybrid quantum system composed of silicon-vacancy color centers (SiV) and diamond acoustic waveguides in a finite-temperature non-Markovian environment. The results indicate that memory parameters, damping rates, environmental temperature, and the total spin number play critical roles in the generation of spin squeezing. By appropriately tuning these parameters, the spin-squeezing effect of the quantum system can be significantly enhanced. This study provides theoretical foundations and optimization strategies for the application of quantum systems in complex environments, such as quantum information processing and quantum precision measurement.
We study entanglement generated between a charge qubit and a bosonic bath due to their joint evolution which leads to pure dephasing of the qubit. We tune the parameters of the interaction, so that the decoherence is quantitatively independent of the number of bosonic modes taken into account and investigate how the entanglement generated depends on the size of the environment. A second parameter of interest is the mixedness of the initial state of the environment which is controlled by temperature. We show analytically that for a pure initial state of the environment, entanglement does not depend on environment size. For mixed initial states of the environment, the generated entanglement decreases with the increase of environment size. This effect is stronger for larger temperatures, when the environment is initially more mixed, but in the limit of an infinitely large environment, no entanglement is created at any finite temperature.
We study the dynamical behavior of two initially entangled qubits, each locally coupled to an environment embodied by an interacting spin chain. We consider energy-exchange qubit–environment couplings resulting in rich and highly non-trivial entanglement dynamics. We obtain exact results for the time evolution of the concurrence between the two qubits and find that, by tuning the interaction parameters, one can freeze the dynamics of entanglement, therefore inhibiting their relaxation into the spin environments, as well as activate a sudden-death phenomenon. We also discuss the effects of an environmental quantum phase transition on the features of the two-qubit entanglement dynamics.