arXiv subjects

C. Rangan

Publications and source records attributed to C. Rangan.

11 recordsLinked to original sources

arXiv2017

Single particle model of a strongly driven, dense, nanoscale quantum ensemble

We study the effects of interatomic interactions on the quantum dynamics of a dense, nanoscale, atomic ensemble driven by a strong electromagnetic field. We use a self-consistent, mean-field technique based on the pseudo-spectral time-domain method, and a full, three-directional basis to solve the coupled Maxwell-Liouville equations. We find that interatomic interactions generate a decoherence in the state of an ensemble on a much faster timescale than the excited state lifetime of individual atoms. We present a novel single-particle model of the driven, dense ensemble by incorporating interactions into a dephasing rate. This single-particle model reproduces the essential physics of the full simulation, and is an efficient way of rapidly estimating the collective dynamics of a dense ensemble.

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arXiv2016

Flag-based Control of Orbit Dynamics in Quantum Lindblad Systems

In this paper, we demonstrate that the dynamics of an $n$-dimensional Lindblad control system can be separated into its inter- and intra-orbit dynamics when there is fast controllability. This can be viewed as a control system on the simplex of density operator spectra, where the flag representing the eigenspaces is viewed as a control variable. The local controllability properties of this control system can be analyzed when the control-set of flags is limited to a finite subset. In particular, there is a natural finite subset of $n!$ flags that are effective for low-purity orbits.

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arXiv2016

Flag-Based Control of Quantum Purity for $n=2$ Systems

This paper investigates the fast Hamiltonian control of $n=2$ density operators by continuously varying the flag as one moves away from the completely mixed state. In general, the critical points and zeros of the purity derivative can only be solved analytically in the limit of minimal purity. We derive differential equations that maintain these features as the purity increases. In particular, there is a thread of points in the Bloch ball that locally maximizes the purity derivative, and a corresponding thread that minimizes it. Additionally, we show there is a closed surface of points inside of which the purity derivative is positive, and inside of which is negative. We argue that this approach may be useful in studying higher-dimensional systems.

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arXiv2009

Finite Controllability of Infinite-Dimensional Quantum Systems

Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin systems, the quantum evolution equation (the Schrödinger equation) is finite-dimensional and old results on controllability of systems defined on on Lie groups and quotient spaces provide most of what is needed insofar as controllability of non-dissipative systems is concerned. However, in an infinite-dimensional setting, controlling the evolution of quantum systems often presents difficulties, both conceptual and technical. In this paper we present a systematic approach to a class of such problems for which it is possible to avoid some of the technical issues. In particular, we analyze controllability for infinite-dimensional bilinear systems under assumptions that make controllability possible using trajectories lying in a nested family of pre-defined subspaces. This result, which we call the Finite Controllability Theorem, provides a set of sufficient conditions for controllability in an infinite-dimensional setting. We consider specific physical systems that are of interest for quantum computing, and provide insights into the types of quantum operations (gates) that may be developed.

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arXiv2008

Controllability and universal three-qubit quantum computation with trapped electron states

We show how to control and perform universal three-qubit quantum computation with trapped electron quantum states. The three qubits are the electron spin, and the first two quantum states of the cyclotron and axial harmonic oscillators. We explicitly show how the universal gates can be performed. As an example of a non-trivial quantum algorithm, we outline the implementation of the Deutsch-Jozsa algorithm in this system.

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arXiv2007

Overcoming the su(2^n) sufficient condition for the coherent control of n-qubit systems

We study quantum systems with even numbers N of levels that are completely state-controlled by unitary transformations generated by Lie algebras isomorphic to sp(N) of dimension N(N+1)/2. These Lie algebras are smaller than the respective su(N) with dimension N^2-1. We show that this reduction constrains the Hamiltonian to have symmetric energy levels. An example of such a system is an n-qubit system. Using a geometric representation for the quantum wave function of a finite system, we present an explicit example that shows a two-qubit system can be controlled by the elements of the Lie algebra sp(4) (isomorphic to spin(5) and so(5)) with dimension ten rather than su(4) with dimension fifteen. These results enable one to envision more efficient algorithms for the design of fields for quantum-state engineering, and they provide more insight into the fundamental structure of quantum control.

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arXiv2006

Control and Representation of n-qubit Quantum Systems

Just as any state of a single qubit or 2-level system can be obtained from any other state by a rotation operator parametrized by three real Euler angles, we show how any state of an n-qubit or 2^n-level system can be obtained from any other by a compact unitary transformation with 2^(n+1)-1 real angles, 2^n of which are azimuthal-like and the rest polar-like. The results follow from a modeling of the Hilbert space of n-qubits by a minimal left ideal of an associative algebra. This representation is expected to be useful in the design of new compact control techniques or more efficient algorithms in quantum computing.

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arXiv2006

Information hiding and retrieval in Rydberg wave packets using half-cycle pulses

We demonstrate an information hiding and retrieval scheme with the relative phases between states in a Rydberg wave packet acting as the bits of a data register. We use a terahertz half-cycle pulse (HCP) to transfer phase-encoded information from an optically accessible angular momentum manifold to another manifold which is not directly accessed by our laser pulses, effectively hiding the information from our optical interferometric measurement techniques. A subsequent HCP acting on these wave packets reintroduces the information back into the optically accessible data register manifold which can then be `read' out.

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arXiv2004

Control of trapped-ion quantum states with optical pulses

We present new results on the quantum control of systems with infinitely large Hilbert spaces. A control-theoretic analysis of the control of trapped ion quantum states via optical pulses is performed. We demonstrate how resonant bichromatic fields can be applied in two contrasting ways -- one that makes the system completely uncontrollable, and the other that makes the system controllable. In some interesting cases, the Hilbert space of the qubit-harmonic oscillator can be made finite, and the Schrödinger equation controllable via bichromatic resonant pulses. Extending this analysis to the quantum states of two ions, a new scheme for producing entangled qubits is discovered.

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arXiv2001

Optimally shaped terahertz pulses for phase retrieval in a Rydberg atom data register

We employ Optimal Control Theory to discover an efficient information retrieval algorithm that can be performed on a Rydberg atom data register using a shaped terahertz pulse. The register is a Rydberg wave packet with one consituent orbital phase-reversed from the others (the ``marked bit''). The terahertz pulse that performs the decoding algorithm does so by by driving electron probability density into the marked orbital. Its shape is calculated by modifying the target of an optimal control problem so that it represents the direct product of all correct solutions to the algorithm.

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arXiv2000

Quantum phase retrieval of a Rydberg wave packet using a half-cycle pulse

A terahertz half-cycle pulse was used to retrieve information stored as quantum phase in an $N$-state Rydberg atom data register. The register was prepared as a wave packet with one state phase-reversed from the others (the "marked bit"). A half-cycle pulse then drove a significant portion of the electron probability into the flipped state via multimode interference.

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