arXiv subjects

Julio Gea-Banacloche

Publications and source records attributed to Julio Gea-Banacloche.

At least 19 recordsLinked to original sources

arXiv2025

Rotation Errors Due to Field Quantization for Simultaneously Driven Atoms

When an electromagnetic field in a coherent or quasiclassical (e.g., squeezed) state is used to simultaneously drive an ensemble of two-level atoms, the quantum nature of the field will, in general, cause the final state of the atoms to differ from the one predicted for a totally classical field. This is a potential source of error in quantum logic gates in which the gate is the rotation of the atoms by a laser. In this paper, we use second order perturbation theory to find how this error scales with the number of atoms, $N$, being driven simultaneously, for an arbitrary rotation angle. The result depends on the initial atomic state: for some highly entangled states, and a field in a coherent state, the error may scale as $N^2$, yet we find that the average over a random distribution of initial states only scales as $N$. We discuss possible ways to mitigate the error, including the use of squeezed states, as well as adjusting the interaction time between the field and atoms to be different from what would be expected from the classical-field treatment.

quant-ph↗

arXiv2024

Large collective power enhancement in dissipative charging of a quantum battery

We consider a model for a quantum battery consisting of a collection of $N$ two-level atoms driven by a classical field and decaying to a common reservoir. In the extensive regime, where the energy $E$ scales as $N$ and the fluctuations $ΔE/E \to 0$, our dissipative charging protocol yields a power proportional to $N^2$, a scaling that cannot be achieved in this regime by Hamiltonian protocols. The tradeoff for this enhanced charging power is a relative inefficiency, since a large fraction of the incoming energy is lost through spontaneous emission to the environment. Nevertheless, we find the system can store a large amount of coherence, and also release the stored energy coherently through spontaneous emission, again with a power scaling as $N^2$.

quant-ph↗

arXiv2024

Recycling of a quantum field and optimal states for single-qubit rotations

We introduce a family of quantized field states that can perform exact (entanglement- and error-free) rotations of a two-level atom starting from a specific state on the Bloch sphere. We discuss the similarities and differences between these states and the recently-introduced "transcoherent states." Our field states have the property that they are left unchanged after the rotation, and we find they are the asymptotic states obtained when a field interacts with a succession of identically prepared ancillary atoms. Such a scheme was recently proposed [npj Quantum Information 3:17 (2017)] as a way to "restore" a field state after its interaction with a two-level atom, so as to reuse it afterwards, thus reducing the energy requirements for successive quantum logical operations. We generalize this scheme to find optimal pulses for arbitrary rotations, and also study analytically what happens if the ancillas are in a mixed, rather than a pure state. Consistent with the numerical results in the original proposal, we find that as long as the ancilla preparation error is small (of the order of $1/\bar n$, where $\bar n$ is the average number of atoms in the pulses considered) it will introduce only higher-order errors in the performance of the restored pulse.

quant-ph↗

arXiv2023

Conditional phase gate between two photons through control of the interaction time with a single atom in a cavity

We show that the simultaneous interaction of two single-photon fields with a single atom in the V configuration can in principle produce a conditional phase gate of arbitrarily high fidelity, for an appropriate choice of the interaction time, as long as the fields con be described by a single temporal mode (as in an optical cavity); this requires a ``gated'' interaction, where, e.g., dynamical coupling techniques could be used to get the fields in and out of the cavity, and a large detuning induced by a strong external field could be used to turn the atom-field interaction on and off at the right times. With these assumptions, our analysis shows that the largest gate fidelities are obtained for a cavity containing a single atom, and that adding more atoms in effect ``dilutes'' the system's nonlinearity. We also study how spontaneous emission losses into non-cavity modes degrade the fidelity, and consider as well a couple of alternate atomic level schemes, namely two- and five-level systems.

quant-ph↗

arXiv2023

Input-output wavepacket description of two photons interacting with a V-type three-level atom in an optical cavity

We study the interaction of a V-type atom in a cavity with incident single- and two-photon wavepackets and derive an exact formula, valid in all parameter regimes, relating the spectrum of the outgoing wavepackets to the incident one. We present detailed results for several special input pulses, and consider the potential performance of the system as a CPHASE gate for initial pulses in a product state. We find values of the cavity, atomic and pulse parameters that yield a conditional phase shift of $π$, albeit with a relatively small overlap between the incoming and outgoing pulse forms.

quant-ph↗

arXiv2022

Stimulated emission of superradiant atoms in waveguide QED

We investigate the stimulated emission of superradiant atoms coupled to a waveguide induced by a coherent-state 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.

quant-ph↗

arXiv2018

Passive, deterministic photonic CPHASE gate via two-level systems

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.

quant-ph↗

arXiv2017

Analytical results for a conditional phase shift between single-photon pulses in a nonlocal nonlinear medium

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 \rangle \longrightarrow i|100 \rangle \longrightarrow -|011 \rangle $. 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.

quant-ph↗

arXiv2017

One- and Two-Photon Scattering by Two Atoms in a Waveguide

We consider the interaction of one- and two-photon pulses in a waveguide with two two-level systems (TLS) that are also able to interact directly either through an exchange- or a dipole-type interaction. We focus on the system's transport properties and show how the presence of a second TLS increases the control options, especially when direct interactions are also allowed. We also obtain, within a Markov (long pulse) approximation, exact results for the nonlinear or entangled terms that arise in the two-photon case, and discuss both their potential applications and ways to minimize their effects.

quant-ph↗

arXiv2017

Two-level atom excitation probability for single- and $N$-photon wavepackets

We study how the transient excitation probability of a two-level atom by a quantized field depends on the temporal profile of the incident pulse, in the presence of external losses, for both coherent and Fock states, and in two complementary limits: when the pulse contains only one photon (on average), and when the number of photons $N$ is large. For the latter case we derive analytical expressions for the scaling of the excitation probability with $N$ that can be easily evaluated for any pulse shape.

quant-ph↗

arXiv2016

Two photons co- and counter-propagating through $N$ cross-Kerr sites

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.

quant-ph↗

arXiv2012

Single-photon, cavity-mediated gates: detuning, losses, and non-adiabatic effects

We study several extensions of the single-photon, cavity-mediated quantum logical gates recently proposed by Koshino, Ishizaka and Nakamura: to a double-sided cavity configuration, to the case where the two atomic ground states are nondegenerate, and to include nonadiabatic corrections. Our analysis can be used to estimate the effects of various imperfections, and to prepare the way for a proof-of-principle demonstration with present technology. An interesting result is that the leading correction to the adiabatic approximation can be made to vanish for a suitable choice of detunings, provided the cavity is "good enough" (high enough ratio of coupling to loss). This could significantly relax the need for long single-photon pulses.

quant-ph↗

arXiv2010

"Modes of the universe" study of two-photon deterministic, passive quantum logical gates

We use the "modes of the universe" approach to study a cavity-mediated two-photon logical gate recently proposed by Koshino, Ishizaka and Nakamura. We clarify the relationship between the more commonly used input-output formalism, and that of Koshino et al., and show that some elements of this gate had been anticipated by other authors. We conclude that their proposed gate can work both in the good and bad cavity limits, provided only that the pulses are long enough. Our formalism allows us to estimate analytically the size of the various error terms, and to follow the spectral evolution of the field + cavity system in the course of the interaction.

quant-ph↗

arXiv2009

Impossibility of large phase shifts via the "giant Kerr effect" with single-photon wavepackets

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 Schrodinger picture is very small as long as the spectral width of the single-photon 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 electromagnetically-induced 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.

quant-ph↗

arXiv2009

Gate fidelity of arbitrary single-qubit gates constrained by conservation laws

Recent investigations show that conservation laws limit the accuracy of gate operations in quantum computing. The inevitable error under the angular momentum conservation law has been evaluated so far for the CNOT, Hadamard, and NOT gates for spin 1/2 qubits, while the SWAP gate has no constraint. Here, we extend the above results to general single-qubit gates. We obtain an upper bound of the gate fidelity of arbitrary single-qubit gates implemented under arbitrary conservation laws, determined by the geometry of the conservation law and the gate operation on the Bloch sphere as well as the size of the ancilla.

quant-ph↗

arXiv2006

Minimum-energy pulses for quantum logic cannot be shared

We show that if an electromagnetic energy pulse with average photon number 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/ . This means that in order to keep the error probability bounded by Nε, with ε~ 1/ , one needs to use N/εphotons, 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.

quant-ph↗

arXiv2005

Effects of random localizing events on matter waves: formalism and examples

A formalism is introduced to describe a number of physical processes that may break down the coherence of a matter wave over a characteristic length scale l. In a second-quantized description, an appropriate master equation for a set of bosonic "modes" (such as atoms in a lattice, in a tight-binding approximation) is derived. Two kinds of "localizing processes" are discussed in some detail and shown to lead to master equations of this general form: spontaneous emission (more precisely, light scattering), and modulation by external random potentials. Some of the dynamical consequences of these processes are considered: in particular, it is shown that they generically lead to a damping of the motion of the matter-wave currents, and may also cause a "flattening" of the density distribution of a trapped condensate at rest.

quant-ph↗

arXiv2005

Mean-field treatment of the damping of the oscillations of a 1D Bose gas in an optical lattice

We present a theoretical treatment of the surprisingly large damping observed recently in one-dimensional 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 fluctuation-dissipation 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 experimentally-observed 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.

cond-mat.other↗