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Acta Physica Polonica A

Qubits in Double Quantum Well Structure

Paweł Jakubczyk, Klaudiusz Majchrowski, Igor E. Tralle

Published Jul 1, 2017• 1 citation
Publisher

Abstract

We propose a new approach to producing the qubits in electron ballistic transport in low-dimensional structures such as double quantum wells or double quantum wires.Next, we examine the possibility to produce quantum entanglement in the framework of the Jaynes-Cummings model and shown that at least in principle, the entanglement can be achieved due to series of "revivals" and "collapses" in the population inversion due to the interaction of a quantized single-mode EM-field with a two-level system.

DOI
10.12693/aphyspola.132.115

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Quantum Entanglement in Double Quantum Systems and Jaynes-Cummings Model

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In the paper, we proposed a new approach to producing the qubits in electron transport in low-dimensional structures such as double quantum wells or double quantum wires (DQW). The qubit could arise as a result of quantum entanglement of two specific states of electrons in DQW structure. These two specific states are the symmetric and antisymmetric (with respect to inversion symmetry) states arising due to tunneling across the structure, while entanglement could be produced and controlled by means of the source of nonclassical light. We examined the possibility to produce quantum entanglement in the framework of Jaynes-Cummings model and have shown that at least in principle, the entanglement can be achieved due to series of "revivals" and "collapses" in the population inversion due to the interaction of a quantized single-mode EM field with a two-level system.

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We extend the study of the Jayne–Cummings (JC) model involving a pair of identical two-level atoms (or qubits) interacting with a single mode quantized field. We investigate the effects of replacing the radiation field mode with a composite spin, comprising [Formula: see text] qubits, or spin-1/2 particles. This model is relevant for physical implementations in superconducting circuit QED, ion trap and molecular systems. For the case of the composite spin prepared in a spin coherent state, we demonstrate the similarities of this set-up to the qubits-field model in terms of the time evolution, attractor states and in particular the collapse and revival of the entanglement between the two qubits. We extend our analysis by taking into account an effect due to qubit imperfections. We consider a difference (or “mismatch”) in the dipole interaction strengths of the two qubits, for both the field mode and composite spin cases. To address decoherence due to this mismatch, we then average over this coupling strength difference with distributions of varying width. We demonstrate in both the field mode and the composite spin scenarios that increasing the width of the “error” distribution increases suppression of the coherent dynamics of the coupled system, including the collapse and revival of the entanglement between the qubits.

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Collapse and revival phenomena in the squeezed state Jaynes-Cummings model

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The dynamic behavior of the inversion of the atomic level occupations has been dissouseed in detail in the process of multiphoton interaction of a two-level atom with a single-mode squeezed coherent state radiation field.

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Dynamics of a two-level atom in a double perpendicular cavity

J. C. García-Melgarejo, N. Lozano-Crisóstomo, Ponciano Rodriguez-Montero +1 more

We propose a variation of the Jaynes-Cummings Model (JCM), which consists of a Two-Level Atom (TLA) within a cross cavity configuration. This new geometry is a suitable tool to understand the origin of new QED features that the original JCM does not reveal, showing revivals in cases where they are not expected to appear. Full Text: PDF References E.T. Jaynes, F.W. Cummings, "Comparison of quantum and semiclassical radiation theories with application to the beam maser", Proc. IEEE 51, 1 (1963). CrossRef M. Wilkens, P. Meystre, "Nonlinear atomic homodyne detection: A technique to detect macroscopic superpositions in a micromaser", Phys. Rev. A 43, 7 (1991). CrossRef I.V. Jyotsna, G.S. Agarwal, "The Jaynes-Cummings model with continuous external pumping", Opt. Commun. 99, 344 (1993). CrossRef M.S. Abdalla, M. Abdel-Aty, A.-S.F. Obada, "Quantum entropy of isotropic coupled oscillators interacting with a single atom", Opt. Comm. 211, 225 (2001). CrossRef M.A. Marchiolli, R.J. Missori, "Qualitative aspects of entanglement in the Jaynes?Cummings model with an external quantum field", J. Phys. A: Math. Gen. 36, 49 (2003). CrossRef J.C. García-Melgarejo, Ph.D. Thesis. INAOE (2015). J.R. Ackerhalt, K. Rzazewski, "Heisenberg-picture operator perturbation theory", Phys. Rev. A 12, 6 (1975) CrossRef J.H. Eberly, N.B. Narozhny, J.J. Sanchez-Mondragon, "Periodic Spontaneous Collapse and Revival in a Simple Quantum Model", Phys. Rev. Lett. 44, 20 (1980). CrossRef N.B. Narozhny, J.J. Sanchez-Mondragon, J.H. Eberly, "Coherence versus incoherence: Collapse and revival in a simple quantum model", Phys. Rev. A 23, 1 (1981). CrossRef L. Allen, J.H. Eberly, Optical resonance and two-level atoms (New York, Wiley 1975). A. Joshi, R.R. Puri, "Effects of the Binomial Field Distribution on Collapse and Revival Phenomena in the Jaynes-Cummings Model", J. Modern Optics 34, 11 (1987). CrossRef

Photonics Letters of Poland•Jul 1, 2015•4 citations
We propose a new approach to producing the qubits in electron ballistic transport in low-dimensional structures such as double quantum wells or double quantum wires.Next, we examine the possibility to produce quantum entanglement in the framework of the Jaynes-Cummings model and shown that at least in principle, the entanglement can be achieved due to series of "revivals" and "collapses" in the population inversion due to the interaction of a quantized single-mode EM-field with a two-level system.
In the paper, we proposed a new approach to producing the qubits in electron transport in low-dimensional structures such as double quantum wells or double quantum wires (DQW). The qubit could arise as a result of quantum entanglement of two specific states of electrons in DQW structure. These two specific states are the symmetric and antisymmetric (with respect to inversion symmetry) states arising due to tunneling across the structure, while entanglement could be produced and controlled by means of the source of nonclassical light. We examined the possibility to produce quantum entanglement in the framework of Jaynes-Cummings model and have shown that at least in principle, the entanglement can be achieved due to series of "revivals" and "collapses" in the population inversion due to the interaction of a quantized single-mode EM field with a two-level system.
Abstract In the photon-atom interaction, one of the most interesting phenomena can be collapse-revival effect in population inversion of atomic levels. Since a single-photon-transition Jaynes–Cummings model can be generalized to a multiphoton-transition Jaynes–Cummings model, of which the Hamiltonian can exhibit a supersymmetric Lie algebra structure, in this paper, quantum collapse and revival in atomic population inversion, which is a collaborative effect of a variety of quantum Rabi oscillations with various quantum Rabi frequencies, is studied for the supersymmetric multiphoton-transition Jaynes–Cummings model. In the literature, it has been pointed out that quantum collapse and revival might find an application in qubit design. We expect that a supersymmetric two-level system might serve as such a kind of qubits. Compared with ordinary two-level qubits, more information could be stored in the basis vectors of supersymmetric qubits, and this could increase the degrees of freedom of tensor product (multi-component extension) of basis vectors of this multiphoton-atom interacting system. For this reason, some characteristics of the collapse-revival effect driven by ordinary coherent states and Yurke–Stoler coherent states will be addressed in this paper. The influence of various characteristic parameters of this supersymmetric Jaynes–Cummings model and the quantized optical fields on the quantum collapse and revival in the population inversion will be indicated in some numerical illustrative examples.
We extend the study of the Jayne–Cummings (JC) model involving a pair of identical two-level atoms (or qubits) interacting with a single mode quantized field. We investigate the effects of replacing the radiation field mode with a composite spin, comprising [Formula: see text] qubits, or spin-1/2 particles. This model is relevant for physical implementations in superconducting circuit QED, ion trap and molecular systems. For the case of the composite spin prepared in a spin coherent state, we demonstrate the similarities of this set-up to the qubits-field model in terms of the time evolution, attractor states and in particular the collapse and revival of the entanglement between the two qubits. We extend our analysis by taking into account an effect due to qubit imperfections. We consider a difference (or “mismatch”) in the dipole interaction strengths of the two qubits, for both the field mode and composite spin cases. To address decoherence due to this mismatch, we then average over this coupling strength difference with distributions of varying width. We demonstrate in both the field mode and the composite spin scenarios that increasing the width of the “error” distribution increases suppression of the coherent dynamics of the coupled system, including the collapse and revival of the entanglement between the qubits.
We propose a variation of the Jaynes-Cummings Model (JCM), which consists of a Two-Level Atom (TLA) within a cross cavity configuration. This new geometry is a suitable tool to understand the origin of new QED features that the original JCM does not reveal, showing revivals in cases where they are not expected to appear. Full Text: PDF References E.T. Jaynes, F.W. Cummings, "Comparison of quantum and semiclassical radiation theories with application to the beam maser", Proc. IEEE 51, 1 (1963). CrossRef M. Wilkens, P. Meystre, "Nonlinear atomic homodyne detection: A technique to detect macroscopic superpositions in a micromaser", Phys. Rev. A 43, 7 (1991). CrossRef I.V. Jyotsna, G.S. Agarwal, "The Jaynes-Cummings model with continuous external pumping", Opt. Commun. 99, 344 (1993). CrossRef M.S. Abdalla, M. Abdel-Aty, A.-S.F. Obada, "Quantum entropy of isotropic coupled oscillators interacting with a single atom", Opt. Comm. 211, 225 (2001). CrossRef M.A. Marchiolli, R.J. Missori, "Qualitative aspects of entanglement in the Jaynes?Cummings model with an external quantum field", J. Phys. A: Math. Gen. 36, 49 (2003). CrossRef J.C. García-Melgarejo, Ph.D. Thesis. INAOE (2015). J.R. Ackerhalt, K. Rzazewski, "Heisenberg-picture operator perturbation theory", Phys. Rev. A 12, 6 (1975) CrossRef J.H. Eberly, N.B. Narozhny, J.J. Sanchez-Mondragon, "Periodic Spontaneous Collapse and Revival in a Simple Quantum Model", Phys. Rev. Lett. 44, 20 (1980). CrossRef N.B. Narozhny, J.J. Sanchez-Mondragon, J.H. Eberly, "Coherence versus incoherence: Collapse and revival in a simple quantum model", Phys. Rev. A 23, 1 (1981). CrossRef L. Allen, J.H. Eberly, Optical resonance and two-level atoms (New York, Wiley 1975). A. Joshi, R.R. Puri, "Effects of the Binomial Field Distribution on Collapse and Revival Phenomena in the Jaynes-Cummings Model", J. Modern Optics 34, 11 (1987). CrossRef