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P. A. Ivanov

Publications and source records attributed to P. A. Ivanov.

8 recordsLinked to original sources
arXiv2016

Spin-1/2 sub-dynamics nested in the quantum dynamics of two coupled qutrits

In this paper we investigate the quantum dynamics of two spin-1 systems, $\vec{\textbf{S}}_1$ and $\vec{\textbf{S}}_2$, adopting a generalized $(\vec{\textbf{S}}_1+\vec{\textbf{S}}_2)^2$-nonconserving Heisenberg model. We show that, due to its symmetry property, the nine-dimensional dynamics of the two qutrits exactly decouples into the direct sum of two sub-dynamics living in two orthogonal four- and five-dimensional subspaces. Such a reduction is further strengthened by our central result consisting in the fact that in the four-dimensional dynamically invariant subspace, the two qutrits quantum dynamics, with no approximations, is equivalent to that of two non interacting spin 1/2's. The interpretative advantages stemming from such a remarkable and non-intuitive nesting are systematically exploited and various intriguing features consequently emerging in the dynamics of the two qutrits are deeply scrutinised. The possibility of exploiting the dynamical reduction brought to light in this paper for exactly treating as well time-dependent versions of our Hamiltonian model is briefly discussed.

quant-ph↗
arXiv2013

Adiabatic quantum metrology with strongly correlated quantum optical systems

We show that the quasi-adiabatic evolution of a system governed by the Dicke Hamiltonian can be described in terms of a self-induced quantum many-body metrological protocol. This effect relies on the sensitivity of the ground state to a small symmetry-breaking perturbation at the quantum phase transition, that leads to the collapse of the wavefunciton into one of two possible ground states. The scaling of the final state properties with the number of atoms and with the intensity of the symmetry breaking field, can be interpreted in terms of the precession time of an effective quantum metrological protocol. We show that our ideas can be tested with spin-phonon interactions in trapped ion setups. Our work points to a classification of quantum phase transitions in terms of the capability of many-body quantum systems for parameter estimation.

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arXiv2010

Scalable quantum search using trapped ions

We propose a scalable implementation of Grover's quantum search algorithm in a trapped-ion quantum information processor. The system is initialized in an entangled Dicke state by using simple adiabatic techniques. The inversion-about-average and the oracle operators take the form of single off-resonant laser pulses, addressing, respectively, all and half of the ions in the trap. This is made possible by utilizing the physical symmetrie of the trapped-ion linear crystal. The physical realization of the algorithm represents a dramatic simplification: each logical iteration (oracle and inversion about average) requires only two physical interaction steps, in contrast to the large number of concatenated gates required by previous approaches. This does not only facilitate the implementation, but also increases the overall fidelity of the algorithm.

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arXiv2009

Simulation of a quantum phase transition of polaritons with trapped ions

We present a novel system for the simulation of quantum phase transitions of collective internal qubit and phononic states with a linear crystal of trapped ions. The laser-ion interaction creates an energy gap in the excitation spectrum, which induces an effective phonon-phonon repulsion and a Jaynes-Cummings-Hubbard interaction. This system shows features equivalent to phase transitions of polaritons in coupled cavity arrays. Trapped ions allow for easy tunabilty of the hopping frequency by adjusting the axial trapping frequency, and the phonon-phonon repulsion via the laser detuning and intensity. We propose an experimental protocol to access all observables of the system, which allows one to obtain signatures of the quantum phase transitions even with a small number of ions.

quant-ph↗
arXiv2008

Robust control of quantized motional states of a chain of trapped ions by collective adiabatic passage

A simple technique for robust generation of vibrational Fock states in a chain of trapped ions is proposed. The method is fast and easy to implement, since only a single chirped laser pulse, simultaneously addressing all of the ions, is required. Furthermore, because the approach uses collective adiabatic passage, significant fluctuations in the intensity or frequency of the laser pulse can be tolerated, and the technique performs well even on the border of the Lamb-Dicke regime. We also demonstrate how this technique may be extended in order to create non-classical superposition states of the ions' collective motion and Greenberger-Horne-Zeilinger states of their internal states. Because only a single laser pulse is required, heating effects arising under realistic experimental conditions are negligibly small.

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arXiv2007

Navigation between quantum states by quantum mirrors

We introduce a technique that allows one to connect any two arbitrary (pure or mixed) superposition states of an N-state quantum system. The proposed solution to this inverse quantum mechanical problem is analytical, exact, and very compact. The technique uses standard and generalized quantum Householder reflections (QHRs), which require external pulses of precise areas and frequencies. We show that any two pure states can be linked by just a single generalized QHR. The transfer between any two mixed states with the same dynamic invariants (e.g., the same density matrix eigenvalues) requires in general N QHRs. Moreover, we propose recipes for synthesis of arbitrary preselected mixed states using a combination of QHRs and incoherent processes (pure dephasing or spontaneous emission).

quant-ph↗
arXiv2007

Engineering of arbitrary U(N) transformations by quantum Householder reflections

We propose a simple physical implementation of the quantum Householder reflection (QHR) M(v)=I-2|v> <v|, which can be produced in the same N-pod system when the fields are appropriately detuned from resonance with the excited state. We use these two operators as building blocks in constructing arbitrary preselected unitary transformations. We show that the most general U(N) transformation can be factorized (and thereby produced) by either N-1 standard QHRs and an N-dimensional phase gate, or N-1 generalized QHRs and a one-dimensional phase gate. Viewed mathematically, these QHR factorizations provide parametrizations of the U(N) group. As an example, we propose a recipe for constructing the quantum Fourier transform (QFT) by at most N interaction steps. For example, QFT requires a single QHR for N=2, and only two QHRs for N=3 and 4.

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