Quantum quenches of ion Coulomb crystals across structural instabilities

Abstract

Quenches in an ion chain can create coherent superpositions of motional states across the linear-zigzag structural transition. The procedure has been described in [Phys. Rev. A 84, 063821 (2011)] and makes use of spin-dependent forces, so that a coherent superposition of the electronic states of one ion evolves into an entangled state between the chain's internal and external degrees of freedom. The properties of the crystalline state so generated are theoretically studied by means of Ramsey interferometry on one ion of the chain. An analytical expression for the visibility of the interferometric measurement is obtained for a chain of arbitrary number of ions and as a function of the time elapsed after the quench. Sufficiently close to the linear-zigzag instability the visibility decays very fast, but exhibits revivals at the period of oscillation of the mode that drives the structural instability. These revivals have a periodicity that is independent of the crystal size, and they signal the creation of entanglement by the quantum quench.

14 pages, 8 figures; added a paragraph in the introduction providing more background, added paragraph at the end of Sec. IV discussing experimental parameters

References in corpus (13)

• Quantum computing with trapped ions
• Decoherence induced by interacting quantum spin baths
• Structural defects in ion crystals by quenching the external potential: the inhomogeneous Kibble-Zurek mechanism
• Ultrafast Gates for Single Atomic Qubits
• Structural phase transitions in low-dimensional ion crystals
• Quantum phase transitions and quantum fidelity in free fermion graphs
• Quantum relaxation after a quench in systems with boundaries
• Measuring entanglement using quantum quenches
• Quantum zigzag transition in ion chains
• Universal decoherence induced by an environmental quantum phase transition
• Double wells, scalar fields and quantum phase transitions in ions traps
• Decoherence induced by a dynamic spin environment (I): The universal regime
• Ramsey interferometry with a spin embedded in a Coulomb chain

Cited by in corpus (5)

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• Trapping Single Ions and Coulomb Crystals with Light Fields
• Determining the squeezing in multimode fields using nonlocal quantum probes
• Operator-based derivation of phonon modes and characterization of correlations for trapped ions at zero and finite temperature
• Dynamical ion transfer between coupled Coulomb crystals in a double well potential