Fock States Research Articles

Dissipation and dephasing of interacting photons in transmon arrays

Transmon arrays are one of the most promising platforms for quantum information science. Despite being often considered simply as qubits, transmons are inherently quantum mechanical multilevel systems. Being experimentally controllable with high fidelity, the higher excited states beyond the qubit subspace provide an important resource for hardware-efficient many-body quantum simulations, quantum error correction, and quantum information protocols. Alas, dissipation and dephasing phenomena generated by couplings to various uncontrollable environments yield a practical limiting factor to their utilization. To quantify this in detail, we present here the primary consequences of single-transmon dissipation and dephasing to the many-body dynamics of transmon arrays. We use analytical methods from perturbation theory and quantum trajectory approach together with numerical simulations, and deliberately consider the full Hilbert space, including the higher excited states. The three main nonunitary processes are many-body decoherence, many-body dissipation, and heating/cooling transitions between different anharmonicity manifolds. Of these, the many-body decoherence---being proportional to the squared distance between the many-body Fock states---gives the strictest limit for observing effective unitary dynamics. Considering experimentally relevant parameters, including also the inevitable site-to-site disorder, our results show that the state-of-the-art transmon arrays should be ready for the task of demonstrating coherent many-body dynamics using the higher excited states. However, the wider utilization of transmons for ternary-and-beyond quantum computing calls for improving their coherence properties.

QCD at the amplitude level: Fock state interference in heavy quark electroproduction

Quantum chromodynamics (QCD) rigorously predicts the existence of both nonperturbative intrinsic and perturbative extrinsic heavy quark contents of nucleons. In this article we discuss the heavy quark electroproduction on protons induced by the Fock states ∣uud + g〉 of three valence quarks in the proton and a nonperturbative gluon, and the mid uud+Qoverline{Q}Bigrangle non-perturbative state of three valence quarks and a heavy quark-antiquark pair. The first one gives the perturbative contribution when the gluon produces a heavy quark pair, while the second is the intrinsic part, and they produce amplitude interference. We use nonperturbative light-front wavefunctions for these Fock states, which are computed using the color-confining light-front holographic QCD theory. Due to interference of the amplitudes corresponding to the intrinsic and extrinsic heavy quark contribution to the proton a novel Q vs. overline{Q} asymmetry emerges in the differential cross section of the electroproduction off a proton {d}^2{sigma}_{e^{-}p}/left( dxd{Q}^2right) . Our analysis proposed a novel asymmetry in QCD between intrinsic and extrinsic heavy quark content in nucleon and provides new insights into the physics of heavy quark phenomena in QCD at the amplitude level. This asymmetry is similar to the Brodsky-Gillespie asymmetry discovered before in QED case and confirmed at DESY.

Hadronic structure on the light front. VI. Generalized parton distributions of unpolarized hadrons

We discuss the generalized parton distributions (GPDs) for unpolarized hadrons, as a continuation of our recent work on hadronic structure on the light front. We analyze the unpolarized GPDs for the light nucleon and delta, as well as generic mesons, using the lowest Fock states. We use these GPDs to reconstruct the charge and gravitational form factors, and discuss their relative sizes. The results are also compared to reported QCD lattice results.

Systematic study of tunable laser cooling for trapped-ion experiments

We report on a comparative analysis of quenched sideband cooling in trapped ions. We introduce a theoretical approach for time-efficient simulation of the temporal cooling characteristics and derive the optimal conditions providing fast laser cooling into the ion’s motional ground state. The simulations were experimentally benchmarked with a single 172Yb+ ion confined in a linear Paul trap. Sideband cooling was carried out on a narrow quadrupole transition, enhanced with an additional clear-out laser for controlling the effective linewidth of the cooling transition. Quench cooling was thus for the first time studied in the resolved sideband, intermediate and semi-classical regime. We discuss the non-thermal distribution of Fock states during laser cooling and reveal its impact on time dilation shifts in optical atomic clocks.

Dress code for infrared safe scattering in QED

Abstract We study the S-matrix and inclusive cross-section for general dressed states in quantum electrodynamics. We obtain an infrared factorization formula of the S-matrix elements for general dressed states. This enables us to study which dressed states lead to infrared-safe S-matrix elements. The condition for dressed states can be interpreted as the memory effect, which is nothing but the conservation law of the asymptotic symmetry. We derive the generalized soft photon theorem for general dressed states. We also compute an inclusive cross-section using general dressed states. It is necessary to use appropriate initial and final dressed states to evaluate interference effects, which cannot be computed correctly by using Fock states due to the infrared divergence.

Proposal for quantum memory miniaturization in superconducting circuit QED

Superconducting circuit quantum electrodynamics is the main architecture for implementation of quantum processors. This work presents a proposal to miniaturize quantum memory devices by combining the quantum memory qubits encoded directly in the first two Fock states ${|0\ensuremath{\rangle},|1\ensuremath{\rangle}}$ and the bus channel in the same specially designed multimode cavity. One key feature of the resonant modes used for quantum memory is that the microwave current is localized, which facilitates the storage and retrieval of information in superconducting qubits while preventing crosstalk from other resonant modes. Frequency design and distinct coupling strengths in this kind of device are analyzed with electromagnetic simulations and numerical calculations. The quantum memory properties, e.g., storage speed, fidelity, and stability, are examined in four cases: (1) memory operation of single-qubit state, (2) disturbing effects, (3) coupling operation, and (4) entangled states storage. Decoherence time of the quantum processor can be extended to more than one order of magnitude longer than that without the memory. By integrating transmons with optimally designed coplanar waveguide multimode quantum memories, the present study could provide an optimistic perspective for the development of large-scale superconducting quantum processors.

Probing the structure of χc1(3872) with photon transition form factors

We propose studying the structure of the ${\ensuremath{\chi}}_{c1}(3872)$ axial vector meson through its ${\ensuremath{\gamma}}_{L}^{*}\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c1}(3872)$ transition form factor. We derive a light-front wave function representation of the form factor for the lowest $c\overline{c}$ Fock state. We found that the reduced width of the state is well within the current experimental bound recently published by the Belle Collaboration. This strongly suggests a crucial role of the $c\overline{c}$ Fock-state in the photon-induced production. Our results for the ${Q}^{2}$ dependence can be tested by future single-tagged ${e}^{+}{e}^{\ensuremath{-}}$ experiments, giving further insight into the short-distance structure of this meson.

Enhancing quantum exchanges between two oscillators

We explore the extent to which two quantum oscillators can exchange their quantum states efficiently through a three-level system which can be spin levels of colored centers in solids. High transition probabilities are obtained using Hamiltonian engineering and quantum control techniques. Starting from a weak coupling approximation, we derive conditions on the spin-oscillator interaction Hamiltonian that enable a high fidelity exhange of quanta. We find that these conditions cannot be fulfilled for arbitrary spin-oscillator coupling. To overcome this limitation, we illustrate how a time-dependent control field applied to the three-level system can lead to an effective dynamic that performs the desired exchange of excitation. In the strong coupling regime, an important loss of fidelity is induced by the dispersion of the excitation onto many Fock states of the oscillators. We show that this detrimental effect can be substantially reduced by suitable control fields, which are computed with optimal control numerical algorithms.

Generating entangled states from coherent states in circuit QED

Entangled states are self-evidently important to a wide range of applications in quantum communication and quantum information processing. We propose an efficient and convenient two-step protocol for generating Bell states and NOON states of two microwave resonators from merely coherent states. In particular, we derive an effective Hamiltonian for resonators coupled to a superconducting $\mathrm{\ensuremath{\Lambda}}$-type qutrit in the dispersive regime. By the excitation-number-dependent Stark shifts of the qutrit transition frequencies, we are able to individually control the amplitudes of specified Fock states of the resonators associated with relevant qutrit transition, using carefully tailored microwave drive signals. Thereby an arbitrary bipartite entangled state in Fock space can be generated by a typical evolution-and-measurement procedure. We analyze the undesired state transitions and the robustness of our protocol against the systematic errors from the microwave driving intensity and frequency, the quantum decoherence of all components, and the crosstalk of two resonators. In addition, we demonstrate that our protocol can be extended to a similar scenario with a $\mathrm{\ensuremath{\Xi}}$-type qutrit.

Adiabatic Amplification of Energy and Magnetic Moment of a Charged Particle after the Magnetic Field Inversion.

We study the evolution of the energy and magnetic moment of a quantum charged particle placed in a homogeneous magnetic field, when this field changes its sign adiabatically. We show that after a single magnetic field passage through zero value, the famous adiabatic invariant ratio of energy to frequency is reestablished again, but with a proportionality coefficient higher than in the initial state. The concrete value of this proportionality coefficient depends on the power index of the frequency dependence on time near zero point. In particular, the adiabatic ratio of the initial ground state (with zero radial and angular quantum numbers) triplicates if the frequency tends to zero linearly as a function of time. If the Larmor frequency attains zero more than once, the adiabatic proportionality coefficient strongly depends on the lengths of the time intervals between zero points, so that the mean energy behavior can be quasi-stochastic after many passages through zero value. The original Born-Fock adiabatic theorem does not work after the frequency passes through zero. However, its generalization is found: the initial Fock state becomes a wide superposition of many instantaneous Fock states, whose weights do not depend on time in the new adiabatic regime.

Microcanonical and canonical fluctuations in atomic Bose-Einstein condensates – Fock state sampling approach

The fluctuations of the atom number between a Bose-Einstein condensate and the surrounding thermal gas have been the subject of a long standing theoretical debate. This discussion is centered around the appropriate thermodynamic ensemble to be used for theoretical predictions and the effect of interactions on the observed fluctuations. Here we introduce the so-called Fock state sampling method to solve this classic problem of current experimental interest for weakly interacting gases. A suppression of the predicted peak fluctuations is observed when using a microcanonical with respect to a canonical ensemble. Moreover, interactions lead to a shift of the temperature of peak fluctuations for harmonically trapped gases. The absolute size of the fluctuations furthermore depends on the total number of atoms and the aspect ratio of the trapping potential. Due to the interplay of these effect, there is no universal suppression or enhancement of fluctuations.

Estimating Fock-state linear optics evolution using coherent states

This paper presents two methods for simulating the interference of bosonic Fock states through linear interferometers using coherent states. The first method repeats the interferometer, injects coherent states in particular modes, and uses symmetric combinations of the outputs to reconstruct the state amplitudes of the Fock-state interference. The second method constructs a new interferometer that can be probed with coherent states on individual inputs to extract the required state amplitudes. The two approaches here show explicitly where the classical computational difficultly arises. In the first approach, the computational hardness is in the measurement post-processing, and in the second approach, it is within the construction of the required state evolution.

Creating large Fock states and massively squeezed states in optics using systems with nonlinear bound states in the continuum

The quantization of the electromagnetic field leads directly to the existence of quantum mechanical states, called Fock states, with an exact integer number of photons. Despite these fundamental states being long-understood, and despite their many potential applications, generating them is largely an open problem. For example, at optical frequencies, it is challenging to deterministically generate Fock states of order two and beyond. Here, we predict the existence of an effect in nonlinear optics, which enables the deterministic generation of large Fock states at arbitrary frequencies. The effect, which we call an n-photon bound state in the continuum, is one in which a photonic resonance (such as a cavity mode) becomes lossless when a precise number of photons n is inside the resonance. Based on analytical theory and numerical simulations, we show that these bound states enable a remarkable phenomenon in which a coherent state of light, when injected into a system supporting this bound state, can spontaneously evolve into a Fock state of a controllable photon number. This effect is also directly applicable for creating (highly) squeezed states of light, whose photon number fluctuations are (far) below the value expected from classical physics (i.e., shot noise). We suggest several examples of systems to experimentally realize the effects predicted here in nonlinear nanophotonic systems, showing examples of generating both optical Fock states with large n (n > 10), as well as more macroscopic photonic states with very large squeezing, with over 90% less noise (10 dB) than the classical value associated with shot noise.

High-probability photon catalysis with non-linear photon beam splitter

Photon catalysis (PC) is an intriguing quantum optical operation wherein the same number of photons are added to and subsequently subtracted from the relevant optical system. It is an important tool that facilitates photon number manipulation. However, most existing PC methods are suitable only for photonic states residing within few-photon subspace. In addition, the probability of PC decreases exponentially with increase in the number n of the Fock state |n〉. Thus, this study proposed a high probability PC scheme for optical quantum states with large Fock state population based on nonlinear beam splitters. The results indicate that the fidelity and the probability of PC are both substantially improved. Moreover, in case of detector inefficiency, the scheme of PC with non-linear beam splitter was more robust. Thus, the proposed method provides a useful tool for manipulating optical quantum states with large Fock number state population.

Nonclassical correlations in lossy cavity optomechanics with intensity-dependent coupling

In this paper, we describe a double-optomechanical system which contains two lossy cavities, where each cavity includes a single-mode quantized field coupled to a single vibrational mode of a flexible membrane. There exists an interaction between a two-level atom and the cavity mode in the rotating wave approximation, with degenerate multi-photon transition in the presence of intensity-dependent coupling. Furthermore, we consider the effect of different sources of dissipation consisting of cavity decay, losses of cavity mirror, and spontaneous emission from the atom. We then start with the master equation to study the dynamics of considered quantum system. Afterward, we show that under some circumstances, the solution of the complicated problem via the master equation is reduced to the determination of the state vector in the time-dependent Schrödinger equation, with the help of an effective non-Hermitian Hamiltonian. Obtaining the explicit form of the state vector of the entire system, we study the nonclassical correlations of two atoms by means of geometric discord. We also examine the roles of intensity-dependent nonlinearity function, number of photons contributed to atomic transition, number of photons in the Fock states, and different sources of dissipation in the dynamics of geometric discord of the atoms. The numerical results indicate that the steady-state value of geometric discord can be revealed, and can appropriately be controlled via the mentioned-above effects. It can be found that the existence of spontaneous emission not only protects the nonclassical correlations of the atoms but also tends the geometric discord to a steady-state value.

Majorization ladder in bosonic Gaussian channels

We show the existence of a majorization ladder in bosonic Gaussian channels, that is, we prove that the channel output resulting from the nth energy eigenstate (Fock state) majorizes the channel output resulting from the (n+1)th energy eigenstate (Fock state). This reflects a remarkable link between the energy at the input of the channel and a disorder relation at its output as captured by majorization theory. This result was previously known in the special cases of a pure-loss channel and quantum-limited amplifier, and we achieve here its non-trivial generalization to any single-mode phase-covariant (or -contravariant) bosonic Gaussian channel. The key to our proof is the explicit construction of a column-stochastic matrix that relates the outputs of the channel for any two subsequent Fock states at its input. This is made possible by exploiting a recently found recurrence relation on multiphoton transition probabilities for Gaussian unitaries [Jabbour and Cerf, Phys. Rev. Res. 3, 043065 (2021)]. Possible generalizations and implications of these results are then discussed.

Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning

^{87} Rb87Rb atoms are known to have long-lived Rydberg excited states with controllable excitation amplitude (detuning) and strong repulsive van der Waals interaction V_{{r} {r'}}Vrr′ between excited atoms at sites {r}r and {r'}r′. Here we study such atoms in a two-leg ladder geometry in the presence of both staggered and uniform detuning with amplitudes \DeltaΔ and \lambdaλ respectively. We show that when V_{{r r'}} \gg(\ll) \Delta, \lambdaVrr′≫(≪)Δ,λ for |{r}-{r'}|=1(>1)|r−r′|=1(>1), these ladders host a plateau for a wide range of \lambda/\Deltaλ/Δ where the ground states are selected by a quantum order-by-disorder mechanism from a macroscopically degenerate manifold of Fock states with fixed Rydberg excitation density 1/41/4. Our study further unravels the presence of an emergent Ising transition stabilized via the order-by-disorder mechanism inside the plateau. We identify the competing terms responsible for the transition and estimate a critical detuning \lambda_c/\Delta=1/3λc/Δ=1/3 which agrees well with exact-diagonalization based numerical studies. We also study the fate of this transition for a realistic interaction potential V_{{r} {r'}} = V_0 /|{r}-{r'}|^6Vrr′=V0/|r−r′|6, demonstrate that it survives for a wide range of V_0V0, and provide analytic estimate of \lambda_cλc as a function of V_0V0. This allows for the possibility of a direct verification of this transition in standard experiments which we discuss.

Production of double heavy quarkonia at super Z factory

Within the color singlet model, we calculate the exclusive production of double charmonia, double bottomonia, and double B_c mesons at future super Z factory. The two heavy quarkonia or B_c’s are either two S-wave Fock states (^1S_0, ~^3S_1), or one S-wave and one P-wave states (^1P_1,~^3P_J~(J=0,1,2)). The top three Z^0 propagated channels in cross sections for double charmonia are sigma {(J/psi +h_c)}_{Z^0}=(454.0^{+39.1}_{-59.2})times 10^{-5} fb, sigma {(eta _c+chi _{c2})}_{Z^0}=(284.2^{+22.2}_{-35.3})times 10^{-5} fb, and sigma {(eta _c+chi _{c0})}_{Z^0}=(137.0^{+9.9}_{-16.4})times 10^{-5} fb. For double bottomonia, they are sigma {(eta _b+Upsilon )}_{Z^0}=(428.6^{+67.9}_{-60.9})times 10^{-4} fb, sigma {(Upsilon +chi _{b2})}_{Z^0}=(230.6^{+23.6}_{-22.2})times 10^{-4} fb, and sigma {(Upsilon +Upsilon )}_{Z^0}=(119.9^{+18.4}_{-16.6})times 10^{-4} fb. For double B_c mesons, they are sigma {(B_c^{*+}+B_c^{*-})}_{Z^0}=(1150^{+87}_{-84})times 10^{-3} fb, sigma {(B_c^{*+}+chi _{bc2}^-)}_{Z^0}=(1133^{-16}_{+22})times 10^{-3} fb, and sigma {(eta _{bc}^++B_c^{*-})}_{Z^0}=(634.6^{+47.8}_{-45.8})times 10^{-3} fb. Here the uncertainties come from the varying masses of constituent heavy quarks, which bring up to 20% corrections. The cross sections of double B_c mesons are roughly one order of magnitude larger than those of the double bottomonia, and two orders of magnitude larger than those of the double charmonia. To make it helpful for experimental study, we present the total cross sections sigma as functions of CM energy sqrt{s}, sigma as functions of the renormalization scale mu , the angle distributions dsigma /dcostheta , and the p_T distributions dsigma /dp_{t}. We also find that the initial state radiation can bring about 30–40% suppresions when 1%m_Z energy is losing, and cross sections can increase by about 2–3 times or decrease by an order of magnitude when adopting different potential models which becomes the major source of uncertainty. The numerical results show that it might be not optimistic for the experimental observation, but it is still far from excluded at the FCC-ee and also the CEPC running in the Z factory mode.

Non-linear Boson Sampling

Boson Sampling is a task that is conjectured to be computationally hard for a classical computer, but which can be efficiently solved by linear-optical interferometers with Fock state inputs. Significant advances have been reported in the last few years, with demonstrations of small- and medium-scale devices, as well as implementations of variants such as Gaussian Boson Sampling. Besides the relevance of this class of computational models in the quest for unambiguous experimental demonstrations of quantum advantage, recent results have also proposed the first applications for hybrid quantum computing. Here, we introduce the adoption of non-linear photon–photon interactions in the Boson Sampling framework, and analyze the enhancement in complexity via an explicit linear-optical simulation scheme. By extending the computational expressivity of Boson Sampling, the introduction of non-linearities promises to disclose novel functionalities for this class of quantum devices. Hence, our results are expected to lead to new applications of near-term, restricted photonic quantum computers.

Infrared divergences in e+e−→2 jets in the light front coherent state formalism

We study infrared (IR) divergences in light front quantum chromodynamics using a coherent state basis in light front time-ordered Hamiltonian perturbation theory. In computation of the S-matrix elements in Hamiltonian formalism, the IR divergences appear in the form of vanishing energy denominators. We consider the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}2$ jets at $\mathcal{O}({g}^{2})$ in strong coupling, construct the coherent state representing the outgoing particles, and explicitly show that the ``true'' IR divergences cancel to this order when the matrix elements are calculated between coherent states instead of Fock states.