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Defect-free single atom array in optical tweezers is a promising platform for scalable quantum computing, quantum simulation, and quantum metrology. Extending single-species array to mixed-species one promise to offer new possibilities. In our recent proof of principle realization of defect-free two-dimensional assembly of mixed-species $^{85}$Rb ($^{87}$Rb) atom arrays [C. Sheng et al.\href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.083202}{{\color{blue} Phys. Rev. Lett. 128, 083202(2022)}}], the filling fractions were limited by the imperfect transfer of atoms and the occurrence of logjams during the atom rearrangement. In order to scale up the size of defect-free mixed-species atom array, we scale up the tweezer array and improve the atom transfer, and upgrade the heuristic heteronuclear algorithm so as to facilitate multiple rearrangement cycles. Consequently, we successfully create defect-free atom arrays with 120 mixed-species single atoms. The corresponding filling fraction and defect-free probability are improved to be 98.6(1)\% and 14(2)\%, respectively. It is anticipated that the enhanced algorithm can be extended to other combinations of atomic species, and this mixed-species atom array is readily for studies of many-body physics, quantum error correction, and quantum metrology., Comment: 8 pages, 5 figures

Arrays of single atoms trapped in optical tweezers are increasingly recognized as a promising platform for scalable quantum computing. In both the fault-tolerant and NISQ eras, the ability to individually control qubits is essential for the efficient execution of quantum circuits. Time-division multiplexed control schemes based on atom shuttling or beam scanning have been employed to build programmable neutral atom quantum processors, but achieving high-rate, highly parallel gate operations remains a challenge. Here, we propose a fiber array architecture for atom quantum computing capable of fully independent control of individual atoms. The trapping and addressing lasers for each individual atom are emitted from the same optical waveguide, enabling robust control through common-mode suppression of beam pointing noise. Using a fiber array, we experimentally demonstrate the trapping and independent control of ten single atoms in two-dimensional optical tweezers, achieving individually addressed single-qubit gate with an average fidelity of 0.9966(3). Moreover, we perform simultaneous arbitrary single-qubit gate on four randomly selected qubits, resulting in an average fidelity of 0.9961(4). Our work paves the way for time-efficient execution of quantum algorithms on neutral atom quantum computers., Comment: 12 pages

Automated market makers are a popular mechanism used on decentralized exchange, through which users trade assets with each other directly and automatically through a liquidity pool and a fixed pricing function. The liquidity provider contributes to the liquidity pool by supplying assets to the pool, and in return, they earn trading fees from investors who trade in the pool. We propose a model of optimal liquidity provision in which a risk-averse liquidity provider decides the amount of wealth she would invest in the decentralized market to provide liquidity in a two-asset pool, trade in a centralized market, and consume in multiple periods. We derive the liquidity provider's optimal strategy and the optimal design of the automated market maker that maximizes the liquidity provider's utility. We find that the optimal unit trading fee increases in the volatility of the fundamental exchange rate of the two assets. We also find that the optimal pricing function is chosen to make the asset allocation in the liquidity pool efficient for the liquidity provider.

The inherent polarization gradients in tight optical tweezers can be used to couple the atomic spins to the two-body motion under the action of a microwave spin-flip transition, so that such a spin-motion coupling offers an important control knob on the motional states of optically trapped two colliding atoms. Here, after preparing two elastically scattering $^{85}$Rb atoms in the three-dimensional ground-state in the optical tweezer, we employed this control in order to probe the colliding energies of elastic and inelastic channels. The combination of microwave spectra and corresponding s-wave pseudopotential model allows us to infer the effect of the state-dependent trapping potentials on the elastic colliding energies, as well as to reveal how the presence of inelastic interactions affects elastic part of the relative potential. Our work shows that the spin-motion coupling in a tight optical tweezer expand the experimental toolbox for fundamental studies of ultracold collisions in the two body systems with reactive collisions, and potentially for that of more complex interactions, such as optically trapped atom-molecule and molecule-molecule interactions., Comment: 8 pages, 5 figures

We propose the first discrete-time infinite-horizon dynamic formulation of the financial index tracking problem under both return-based tracking error and value-based tracking error. The formulation overcomes the limitations of existing models by incorporating the intertemporal dynamics of market information variables not limited to prices, allowing exact calculation of transaction costs, accounting for the tradeoff between overall tracking error and transaction costs, allowing effective use of data in a long time period, etc. The formulation also allows novel decision variables of cash injection or withdraw. We propose to solve the portfolio rebalancing equation using a Banach fixed point iteration, which allows to accurately calculate the transaction costs specified as nonlinear functions of trading volumes in practice. We propose an extension of deep reinforcement learning (RL) method to solve the dynamic formulation. Our RL method resolves the issue of data limitation resulting from the availability of a single sample path of financial data by a novel training scheme. A comprehensive empirical study based on a 17-year-long testing set demonstrates that the proposed method outperforms a benchmark method in terms of tracking accuracy and has the potential for earning extra profit through cash withdraw strategy., Comment: 75 pages,15 figures, and 13 tables

The development of a microwave electrometer with inherent uncertainty approaching its ultimate limit carries both fundamental and technological significance. Recently, the Rydberg electrometer has garnered considerable attention due to its exceptional sensitivity, small-size, and broad tunability. This specific quantum sensor utilizes low-entropy laser beams to detect disturbances in atomic internal states, thereby circumventing the intrinsic thermal noise encountered by its classical counterparts. However, due to the thermal motion of atoms, the advanced Rydberg-atom microwave electrometer falls considerably short of the standard quantum limit by over three orders of magnitude. In this study, we utilize an optically thin medium with approximately 5.2e5 laser-cooled atoms to implement heterodyne detection. By mitigating a variety of noises and strategically optimizing the parameters of the Rydberg electrometer, our study achieves an electric-field sensitivity of 10.0 nV/cm/Hz^1/2 at a 100 Hz repetition rate, reaching a factor of 2.6 above the standard quantum limit and a minimum detectable field of 540 pV/cm. We also provide an in-depth analysis of noise mechanisms and determine optimal parameters to bolster the performance of Rydberg-atom sensors. Our work provides insights into the inherent capacities and limitations of Rydberg electrometers, while offering superior sensitivity for detecting weak microwave signals in numerous applications., Comment: 12 pages

Single atoms are interesting candidates for studying quantum optics and quantum information processing. Recently, trapping and manipulation of single atoms using tight optical dipole traps have generated considerable interest. Here we report an experimental investigation of the dynamics of atoms in a modified optical dipole trap with a backward propagating dipole trap beam, where a change in the two-atom collision rate by six times has been achieved. The theoretical model presented gives a prediction of high probabilities of few-atom loading rates under proper experimental conditions. This work provides an alternative approach to the control of the few-atom dynamics in a dipole trap and the study of the collective quantum optical effects of a few atoms., Comment: 5 pages, 3 figures

Complex systems are embedded in our everyday experience. Stochastic modelling enables us to understand and predict the behaviour of such systems, cementing its utility across the quantitative sciences. Accurate models of highly non-Markovian processes -- where the future behaviour depends on events that happened far in the past -- must track copious amounts of information about past observations, requiring high-dimensional memories. Quantum technologies can ameliorate this cost, allowing models of the same processes with lower memory dimension than corresponding classical models. Here we implement such memory-efficient quantum models for a family of non-Markovian processes using a photonic setup. We show that with a single qubit of memory our implemented quantum models can attain higher precision than possible with any classical model of the same memory dimension. This heralds a key step towards applying quantum technologies in complex systems modelling., Comment: 11+2 pages, 5 figures

Dual-species single-atom array in optical tweezers has several advantages over the single-species atom array as a platform for quantum computing and quantum simulation. Thus, creating the defect-free dual-species single-atom array with atom numbers over hundreds is essential. As recent experiments demonstrated, one of the main difficulties lies in designing an efficient algorithm to rearrange the stochastically loaded dual-species atoms arrays into arbitrary demanded configurations. We propose a heuristic connectivity optimization algorithm (HCOA) to provide the near-fewest number of atom moves. Our algorithm introduces the concept of using articulation points in an undirected graph to optimize connectivity as a critical consideration for arranging the atom moving paths. Tested in array size of hundreds atoms and various configurations, our algorithm shows a high success rate (> 97%), low extra atom moves ratio, good scalability, and flexibility. Furthermore, we proposed a complementary step to solve the problem of atom loss during the rearrangement.

We consider a generalization of the recursive utility model by adding a new component that represents utility of investment gains and losses. We also study the utility process in this generalized model with constant elasticity of intertemporal substitution and relative risk aversion degree, and with infinite time horizon. In a specific, finite-state Markovian setting, we prove that the utility process uniquely exists when the agent derives nonnegative gain-loss utility, and that it can be non-existent or non-unique otherwise. Moreover, we prove that the utility process, when it uniquely exists, can be computed by starting from any initial guess and applying the recursive equation that defines the utility process repeatedly. We then consider a portfolio selection problem with gain-loss utility and solve it by proving that the corresponding dynamic programming equation has a unique solution. Finally, we extend certain previous results to the case in which the state space is infinite.

Time inconsistency is prevalent in dynamic choice problems: a plan of actions to be taken in the future that is optimal for an agent today may not be optimal for the same agent in the future. If the agent is aware of this intra-personal conflict but unable to commit herself in the future to following the optimal plan today, the rational strategy for her today is to reconcile with her future selves, namely to correctly anticipate her actions in the future and then act today accordingly. Such a strategy is named intra-personal equilibrium and has been studied since as early as in the 1950s. A rigorous treatment in continuous-time settings, however, had not been available until a decade ago. Since then, the study on intra-personal equilibrium for time-inconsistent problems in continuous time has grown rapidly. In this chapter, we review the classical results and some recent development in this literature.

We consider portfolio optimization under a preference model in a single-period, complete market. This preference model includes Yaari's dual theory of choice and quantile maximization as special cases. We characterize when the optimal solution exists and derive the optimal solution in closed form when it exists. The payoff of the optimal portfolio is a digital option: it yields an in-the-money payoff when the market is good and zero payoff otherwise. When the initial wealth increases, the set of good market scenarios remains unchanged while the payoff in these scenarios increases. Finally, we extend our portfolio optimization problem by imposing a dependence structure with a given benchmark payoff and derive similar results., Comment: arXiv admin note: substantial text overlap with arXiv:2008.10257

Although maximizing median and quantiles is intuitively appealing and has an axiomatic foundation, it is difficult to study the optimal portfolio strategy due to the discontinuity and time inconsistency in the objective function. We use the intra-personal equilibrium approach to study the problem. Interestingly, we find that the only viable outcome is from the median maximization, because for other quantiles either the equilibrium does not exist or there is no investment in the risky assets. The median maximization strategy gives a simple explanation to why wealthier people invest more percentage of their wealth in risky assets.

In this paper, we prove a sufficient and necessary condition for the transition probability distribution of a general, time-inhomogeneous linear SDE to possess a density function and study the differentiability of the density function and the transition quantile function of the SDE. Moreover, we completely characterize the support of the marginal distribution of this SDE.

We introduce the concept of forward rank-dependent performance processes, extending the original notion to forward criteria that incorporate probability distortions. A fundamental challenge is how to reconcile the time-consistent nature of forward performance criteria with the time-inconsistency stemming from probability distortions. For this, we first propose two distinct definitions, one based on the preservation of performance value and the other on the time-consistency of policies and, in turn, establish their equivalence. We then fully characterize the viable class of probability distortion processes, providing a bifurcation-type result. Specifically, it is either the case that the probability distortions are degenerate in the sense that the investor would never invest in the risky assets, or the marginal probability distortion equals to a normalized power of the quantile function of the pricing kernel. We also characterize the optimal wealth process, whose structure motivates the introduction of a new, distorted measure and a related market. We then build a striking correspondence between the forward rank-dependent criteria in the original market and forward criteria without probability distortions in the auxiliary market. This connection also provides a direct construction method for forward rank-dependent criteria. A byproduct of our work are some new results on the so-called dynamic utilities and on time-inconsistent problems in the classical (backward) setting.