Papers by Julio Gea-banacloche
Physical Review A
We consider the application of the entanglement criteria derived by Hillery and Zubairy [Phys. Re... more We consider the application of the entanglement criteria derived by Hillery and Zubairy [Phys. Rev. Lett. 96, 050503 (2006)] to the detection of entanglement in N-qubit systems. For N = 2 qubits we show that, with the natural choice of operators, one of the criteria never detects entanglement; we also derive conditions for the other criterion to work and for it to have a simple relation to the negativity when it does. For general angular momenta we show the Hillery-Zubairy relations can always detect the entanglement of the (pure) states of well-defined total (J, J z) if the "test" operators are chosen appropriately. We then show how this may be used, in particular, to develop useful criteria to detect entanglement in a system of N two-level atoms interacting with a field initially in a number state (the Tavis-Cummings model).
Physical Review Letters, 1987
It is predicted that a laser's phase-diffusion rate (its Schawlow-Townes linewidth) may be reduce... more It is predicted that a laser's phase-diffusion rate (its Schawlow-Townes linewidth) may be reduced by as much as one-half when the laser is coupled out to "squeezed vacuum" as opposed to ordinary vacuum. The eftect is important because it is directly related to spontaneous emission in a squeezed vacuum. It shows that a part of spontaneous emission is due to amplified zero-point noise and that, therefore, in a squeezed field the random phases of the spontaneously emitted photons are no longer uniformly distributed.
Conference on Lasers and Electro-Optics, Mar 14, 2022
We investigate the stimulated emission of superradiant atoms coupled to a waveguide induced by a ... more We investigate the stimulated emission of superradiant atoms coupled to a waveguide induced by a coherentstate photon pulse. We provide an analytical result when a short π pulse is incident, which shows that the atoms emit photons coherently into the output pulse, which remains a coherent state in the short pulse limit. An incident pulse is amplified in phase-preserving manner, where noise is added almost entirely in the phase direction in phase space. This property improves the ratio of intensity signal to noise after the amplification for sufficiently short pulses. This is a unique feature different from general phase-preserving linear amplifiers, where the signal-to-noise ratio deteriorates in the amplification process. We also discuss the dependence of the photon-emission probability on pulse parameters, such as the pulse area and the duration.
Physical Review A, 2018
It has been suggested that second-order nonlinearities could be used for quantum logic at the sin... more It has been suggested that second-order nonlinearities could be used for quantum logic at the single-photon level. Specifically, successive two-photon processes in principle could accomplish the phase shift (conditioned on the presence of two photons in the low frequency modes) |011 −→ |100 −→ −|011. We have analyzed a recent scheme proposed by Xia et al. to induce such a conditional phase shift between two single-photon pulses propagating at different speeds through a nonlinear medium with a nonlocal response. We present here an analytical solution for the most general case, i.e. for an arbitrary response function, initial state, and pulse velocity, which supports their numerical observation that a π phase shift with unit fidelity is possible, in principle, in an appropriate limit. We also discuss why this is possible in this system, despite the theoretical objections to the possibility of conditional phase shifts on single photons that were raised some time ago by Shapiro and by one of us.
Physical Review A, 2019
We show that an array of identical two level systems coupled losslessly to a one dimensional wave... more We show that an array of identical two level systems coupled losslessly to a one dimensional waveguide is able to realize a high fidelity conditional phase shift useful for quantum logic. We propose two arrangements of emitters (one that relies on direct interactions between the emitters, and one that does not), and describe possible physical realizations and limitations.
Physical Review A, 2015
A second-order nonlinearity has been proposed as a way to perform a conditional phase gate betwee... more A second-order nonlinearity has been proposed as a way to perform a conditional phase gate between two photons. The process involves combining the two photons into a single one (parametric up-conversion) and subsequently splitting that one into two photons identical to the original ones (parametric down-conversion), except for an overall phase shift. We show here that, when the multimode nature of the initial photon wavepackets is considered, this approach suffers from the same difficulties as the third-order (Kerr-based) methods: specifically, the final state of the photons is inevitably spectrally distorted and entangled. The maximum fidelity appears to be limited to F < 0.4 for a free-space configuration, but we find that this could theoretically be pushed to F ≃ 0.6 if the nonlinear medium is placed in an optical cavity. We show analytically that this latter result is identical to what one would obtain from a third-order nonlinear medium in the same arrangement.
Physical Review A, 2016
A cross-Kerr interaction produces a phase shift on two modes of light proportional to the number ... more A cross-Kerr interaction produces a phase shift on two modes of light proportional to the number of photons in both modes, and is sometimes called cross-phase modulation. Cross-Kerr nonlinearities have many applications in classical and quantum nonlinear optics, including the possibility of a deterministic and all-optical controlled-phase gate. We calculate the one-and two-photon S-matrix for fields propagating in a medium where the cross-Kerr interaction is spatially distributed at discrete interaction sites comprised of atoms. For the interactions considered, we analyze the cases where the photons co-propagate and counter-propagate through the medium and give a physical interpretation to the differences between the two cases. Finally, we obtain the S-matrix in the limit of infinitely long chains, showing that it corresponds to a perfect controlled-phase operation.
A lower bound on the amount of energy needed to carry out an elementary logical operation on a qu... more A lower bound on the amount of energy needed to carry out an elementary logical operation on a qubit system, with a given accuracy and in a given time, has been recently postulated. This paper is an attempt to formalize this bound and explore the conditions under which it may be expected to hold. This is a work in progress and any contributions will be appreciated.
Erratum: Quantum error correction against correlated noise [Phys. Rev. A 69 , 062313 (2004)]
Physical Review A, 2004
Physical Review A, 2010
An approximate analytical solution is presented, along with numerical calculations, for a system ... more An approximate analytical solution is presented, along with numerical calculations, for a system of two single-photon wavepackets interacting via an ideal, localized Kerr medium. It is shown that, because of spontaneous emission into the initially unoccupied temporal modes, the cross-phase modulation in the Schrödinger picture is very small as long as the spectral width of the singlephoton pulses is well within the medium's bandwidth. In this limit, the Hamiltonian used can be derived from the "giant Kerr effect" for a four-level atom, under conditions of electromagneticallyinduced transparency; it is shown explicitly that the linear absorption in this system increases as the pulse's spectral width approaches the medium's transparency bandwidth, and hence, as long as the absorption probability remains small, the maximum cross-phase modulation is limited to essentially useless values. These results are in agreement with the general, causality-and unitarity-based arguments of Shapiro and co-workers. II. INSTANTANEOUS RESPONSE LIMIT A. Hamiltonian, locality, and Heisenberg picture results Suppose that, somehow, one has managed to produce a medium that leads, to a sufficiently good approximation, to a field evolution described by the following Hamilto
Quantum Information and Computation IV, 2006
We have studied the performance of a geometric phase gate with a quantized driving field numerica... more We have studied the performance of a geometric phase gate with a quantized driving field numerically, and developed an analytical approximation that yields some preliminary insight on the way the nl~hlt becomes entangled with the driving field.
Physical Review A, 2006
We present a theoretical treatment of the surprisingly large damping observed recently in onedime... more We present a theoretical treatment of the surprisingly large damping observed recently in onedimensional Bose-Einstein atomic condensates in optical lattices. We show that time-dependent Hartree-Fock-Bogoliubov (HFB) calculations can describe qualitatively the main features of the damping observed over a range of lattice depths. We also derive a formula of the fluctuationdissipation type for the damping, based on a picture in which the coherent motion of the condensate atoms is disrupted as they try to flow through the random local potential created by the irregular motion of noncondensate atoms. We expect this irregular motion to result from the well-known dynamical instability exhibited by the mean-field theory for these systems. When parameters for the characteristic strength and correlation times of the fluctuations, obtained from the HFB calculations, are substituted in the damping formula, we find very good agreement with the experimentallyobserved damping, as long as the lattice is shallow enough for the fraction of atoms in the Mott insulator phase to be negligible. We also include, for completeness, the results of other calculations based on the Gutzwiller ansatz, which appear to work better for the deeper lattices.
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Proceedings of the IEEE, 2010
I t has been about 15 years since twin discoveries by Peter Shor, then at Bell Laboratories, sudd... more I t has been about 15 years since twin discoveries by Peter Shor, then at Bell Laboratories, suddenly turned quantum computing into the extremely active research field that it remains to this day. The first one was, of course, his celebrated factoring algorithm, which showed that quantum computers could, in principle, solve a task of great cryptographic importance using exponentially fewer steps than the best currently known algorithms running on conventional computers [1]. The second discovery, however, was perhaps even more significant for physicists: it was the remarkable realization that quantum error-correcting codes existed [2], [8] that could (again in principle) make quantum computation fault tolerant. This meant that it would be possible to protect quantum information from decoherence, which had been regarded, up until that point, as the chief obstacle to the eventual realization of quantum computers.
Physical Review Letters, 2002
A lower bound on the amount of energy needed to carry out an elementary logical operation on a qu... more A lower bound on the amount of energy needed to carry out an elementary logical operation on a quantum computer, with a given accuracy and in a given time, is derived. The bound arises from the requirement that the controls used to manipulate the qubits, which ultimately are themselves quantum mechanical systems, must nonetheless be classical to a sufficiently good approximation; it is expected to hold under a wide variety of conditions, and independently of the nature of the physical systems used to encode the qubits. This could have important consequences for very large-scale quantum computations.
Physical Review B, 2005
Recent experiments on quantum behavior in microfabricated solid-state systems suggest tantalizing... more Recent experiments on quantum behavior in microfabricated solid-state systems suggest tantalizing connections to quantum optics. Several of these experiments address the prototypical problem of cavity quantum electrodynamics: a two-level system coupled to a quantum harmonic oscillator. Such devices may allow the exploration of parameter regimes outside the near-resonance and weakcoupling assumptions of the ubiquitous rotating-wave approximation (RWA), necessitating other theoretical approaches. One such approach is an adiabatic approximation in the limit that the oscillator frequency is much larger than the characteristic frequency of the two-level system. A derivation of the approximation is presented, together with a discussion of its applicability in a system consisting of a Cooper-pair box coupled to a nanomechanical resonator. Within this approximation the time evolution of the two-level-system occupation probability is calculated using both thermaland coherent-state initial conditions for the oscillator, focusing particularly on collapse and revival phenomena. For thermal-state initial conditions parameter regimes are found in which collapse and revival regions may be clearly distinguished, unlike the erratic evolution of the thermal-state RWA model. Coherent-state initial conditions lead to complex behavior, which exhibits sensitive dependence on the coupling strength and the initial amplitude of the oscillator state. One feature of the regime considered here is that closed-form evaluation of the time evolution may be carried out in the weak-coupling limit, which provides insight into the differences between the thermal-and coherentstate models. Finally, potential experimental observations in solid-state systems, particularly the Cooper-pair box-nanomechanical resonator system, are discussed and found to be promising.
Physical Review B, 2014
The familiar Rabi model, comprising a two-level system coupled to a quantum harmonic oscillator, ... more The familiar Rabi model, comprising a two-level system coupled to a quantum harmonic oscillator, continues to produce rich and surprising physics when the coupling strength becomes comparable to the individual subsystem frequencies. We construct approximate solutions for the eigenstates and energies in the regime in which the oscillator frequency is small compared to that of the two-level system and the coupling strength matches or exceeds the oscillator frequency. The resulting oscillator dynamics closely resembles that of a particle tunneling in a classical double-well potential. Relating our calculation to an earlier semiclassical approximation in which coupling to the two-level system creates an effective potential for the oscillator, we examine the extent to which this picture is valid. We find that, for certain parameter regimes, the interpretation of the oscillator dynamics in terms of tunneling holds to a good approximation despite the fundamentally entangled nature of the joint system. We assess the prospects for observation of oscillator tunneling in the context of nano-or micromechanical experiments and find that it should be possible if suitably high coupling strengths can be engineered.
Physical Review A, 2006
We show that if an electromagnetic energy pulse with average photon numbern is used to carry out ... more We show that if an electromagnetic energy pulse with average photon numbern is used to carry out the same quantum logical operation on a set of N atoms, either simultaneously or sequentially, the overall error probability in the worst case scenario (i.e., maximized over all the possible initial atomic states) scales as N 2 /n. This means that in order to keep the error probability bounded by N ǫ, with ǫ ∼ 1/n, one needs to use Nn photons, or equivalently N separate "minimum-energy" pulses: in this sense the pulses cannot, in general, be shared. The origin for this phenomenon is found in atom-field entanglement. These results may have important consequences for quantum logic and, in particular, for large-scale quantum computation.
Physical Review A, 2001
We show a way to correct collective error through a three-qubit quantum code. The encoding and de... more We show a way to correct collective error through a three-qubit quantum code. The encoding and decoding ͑i.e., error recovery͒ operations for such a code, which protects one qubit of quantum information perfectly ͑with infinite ''distance''͒ against collective decoherence, are presented. The code is actually a manifestation of a noiseless subsystem first reported by Knill, Laflamme, and Viola ͓Phys. Rev. Lett. 84, 2525 ͑2000͔͒, and provides a good illustration of the relationship between noiseless subsystems and error-correcting codes already noted by these authors. We also show in detail how this code can be used to preserve an arbitrary joint state ͑including entangled states͒ of two qubits, by pairing each of them with two other qubits, even in the case in which the two resulting clusters interact in nonequivalent ways with a common environment.
Physical Review A, 1993
An approximate solution is given for the Jaynes-Cummings model with cavity losses, i.e. , the pro... more An approximate solution is given for the Jaynes-Cummings model with cavity losses, i.e. , the problem of a two-level atom interacting with a single mode of the quantized radiation field, in the rotating-wave approximation, when the field is damped by a reservoir at zero temperature. The approximate solution is derived for initial coherent field states with moderately large numbers of photons. It is simpler in form than earlier results derived by other authors and, over the appropriate parameter range, substantially more accurate than some of them, as shown by direct numerical integration of the master equation. In particular, it is found that an earlier treatment of this problem based on a secular approximation is seriously Qawed, in that the conditions for its validity are much more restrictive than was previously believed. Among the results derived it is shown that, just as for the lossless case, when the atom is initially prepared in one of the semiclassical eigenstates the evolution is very simple, with the field and the atomic dipole drifting together in phase. For moderate losses this leads, as in the lossless case, to a "state preparation"; i.e. , to a good approximation, the state of the atom at a specific time can be made independent of its initial state. The e6'ect of losses on the recently discovered "Schrodinger cat" state of the field is also analyzed. It is found that, although the dissipation destroys the coherence of the macroscopic superposition very rapidly, preparation and observation of the "cat" should be possible with the cavity quality factors reported in recent micromaser experiments.
Physical Review A, 2002
The quantum nature of the laser fields used in many proposed schemes for the manipulation of quan... more The quantum nature of the laser fields used in many proposed schemes for the manipulation of quantum information may have important consequences for some very large scale quantum computations. Some of these consequences are explored here, focusing especially on phase errors and their effects on error-correction schemes. Depending on the way the logical gates are performed, constraints are found on either the required number of photons per coherence time put out by the laser source, or the source's power
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Papers by Julio Gea-banacloche