Quantum Frontiers | Quantum computation and simulation based on 'Rydberg atoms'

Keith Cooper has written, "If the rapidly growing field of atomic physics continues to succeed, future quantum computers could run on energy transitions from excited atoms, or even on pure light."

For physicists chasing the holy grail of quantum computing, a "tasty" recipe is becoming increasingly common. Sprinkle a handful of atoms (rubidium is a common ingredient) into a vacuum chamber, cool the atoms to a fraction above absolute zero with a laser beam, and add a few photons to make one of the basic building blocks of a quantum computer.

Ultracold optical lattice forms a trap for Rydberg atoms

--At the heart of all this is the Rydberg atom, which has an outer valence electron that can be excited to higher quantum states. They are the "big daddy" of the atomic world: the nucleus is usually only a few micrometers in size, but in Rydberg atoms the excited valence electrons can leave the nucleus by a few micrometers while remaining bound to it, which extends the radius of the atom by a factor of a billion. With such a large range, the Rydberg atom can interact with other nearby atoms through a powerful electric dipole moment that is a million times more effective than that of a "normal" atom. It is this ability to interact, and to control it with a carefully chosen photon, that makes the Rydberg atom such a powerful force in the field of quantum information systems.

/Catalog/

I. What are Rydberg atoms?
II. quantum computation using Rydberg atoms
2.1. Physical quantum bits and their coherence times
2.2. Scalability of Neutral Atom Systems
2.3. Initialization and state detection in computation
III. Rydberg-mediated quantum gates
IV. quantum simulations using Rydberg atoms
4.1. Coherent Spin Models
4.2. Dynamics of Atomic and Electronic Motion
4.3. Many-Body Physics of Dissipative Systems
V. Quantum Optics Based on Rydberg Atoms
VI. Scalable Quantum Computers, Sprouting from Rydberg Atoms

Rydberg atoms are highly excited state atoms whose outer electrons are excited to a large principal quantum number n. Due to some properties not possessed by other neutral atoms, such as larger orbital radius, longer radiation lifetime and stronger electric dipole moment, Rydberg atoms have important applications in the field of quantum information.

In 1885, the Swiss physicist Johann Balmer discovered that the width of the spectral lines of the hydrogen atom could be expressed in a simple form. Subsequently, in 1890, the Swedish physicist Johannes Rydberg modified Balmer's empirical formula in the form of a wave number (the reciprocal of wavelength) and gave a formula for the binding energy of the hydrogen atom:

where Ry is the Rydberg constant, and the Rydberg constant for the hydrogen atom is 13.6 eV. With the establishment of Bohr's model of the atom, it was further determined in 1913 that n in the formula was the principal quantum number of the atom. Bohr found that the Rydberg constant was related to additional fundamental physical constants and gave specific expressions for the Rydberg constant:

where Z is the atomic nuclear charge, e is the electron charge, me is the electron mass, ε0 is the vacuum dielectric constant, and ћ is Planck's constant. On this basis combined with the Rydberg formula one can calculate the energy of the Rydberg state with a very large principal quantum number n.

The Rydberg state means that the electrons outside the nucleus are farther away from the nucleus (which can be much larger than the size of the nucleus), so the Rydberg state has a high ionization energy, is easy to interact with microwave fields, radiofrequency electric fields, and classical laser fields, and has a long lifetime. Atoms with Rydberg states are called Rydberg atoms. Rydberg atoms have dipole-dipole interactions, i.e., long-range van der Waals forces.

Among the many properties of Rydberg atoms, the most widely studied are the strong long-range interactions. For atoms trapped in optical lattices or ultracold atoms, the interactions between them are small and essentially negligible, e.g., less than 1 Hz between two atoms separated by 1 μm.

The interaction between Rydberg atoms, on the other hand, behaves as a van der Waals interaction when the atomic spacing is small, proportional to n⁶, and as a resonant dipole-dipole interaction when the atomic spacing is large, proportional to n³. The Rydberg atoms interact strongly because of their large principal quantum number n.

Unlike the Coulombic interactions between trapped ions, the interactions between Rydberg atoms vary in strength over a wide range and can be controlled by coupled optical fields, which makes them significantly superior to trapped ions and ordinary neutral atoms in realizing various quantum gate operations.

The Rydberg atom is a promising physical system for realizing quantum computers because of its long-lived Rydberg states and extremely strong Rydberg interatomic interactions. The long-lived Rydberg state is particularly well suited for storing quantum information, and it greatly reduces the effect of the atom's spontaneous radiation on quantum information. Strong Rydberg interatomic interactions can directly couple two atoms, which is highly conducive to the realization of double-bit gates or interatomic entanglement.

The use of Rydberg atom interactions allows the transfer of entangled states between multiple atoms through excited state transfer in addition to more optimized multi-atom entanglement.

In addition, strong interactions between Rydberg atoms induce an effect of suppressed excitation called dipole blocking, i.e., within a certain range, if an atom is excited to a Rydberg state, the excitation of other atoms in the neighborhood is suppressed.

A system of Rydberg atoms confined within the radius of the Rydberg blockage allows only one Rydberg atom to be excited to the Rydberg state, resulting in the formation of a mesoscopic scale (the scale between the macroscopic and microscopic) Rydberg superatom. It is easier to prepare Rydberg superatoms than Rydberg monatoms, and the collective low-energy states of Rydberg superatoms are particularly well suited to encode quantum bits, which are more robust to leakage of atoms than those encoded by single atoms.

The blocking effect was first observed in the ⁸⁷Rb (rubidium) atomic gas in 2004 by British physicist David Tong et al. It was subsequently shown that Förster resonance can enhance this dipole blocking effect.

Energy levels and electron probability density of 87Rb atoms.

Rydberg interaction and Rydberg blockade. (a) Dipole-dipole interaction between two atoms with atomic spacing R and angle θ with the quantization axis z. (c) Rydberg blockade in the two-atom case. (d) Rydberg superatom in an atomic ensemble. All atoms in a volume of radius Rb share a Rydberg excitation.

Since then, the research work no longer only stops at experimentally observing the blocking effect, but people have also proposed many schemes to widely apply the blocking effect to the field of quantum information. For example, the blocking effect of the Rydberg atomic system can be utilized to realize quantum gate operation, prepare entangled states, prepare single-photon sources and realize quantum simulators.

We can understand how the basic neutral atom quantum computing platform works by breaking down the complex quantum information processing system into a series of manageable subsystems following a hierarchical quantum computer architecture.

At the physical layer, atoms evolve with control sequences such as atom cooling and loading, quantum bit initialization and detection, quantum gates, loss detection and reloading. At the virtual layer, open-loop quantum control techniques (e.g., dynamic decoupling) are used to increase the coherence time. Among them, the DiVincenzo criterion embodies the basic requirements of the first two layers.

Limited by the proven shortcomings of quantum gate operations, few theoretical studies have been reported at the quantum error correction (QEC) layer or beyond. Nevertheless, some near-term applications can be developed in the noise-containing intermediate-scale quantum computing (NISQ) regime.

1) Physical quantum bits and their coherence times

Theoretically, any quantum system with more than two distinguishable states can be used to encode quantum bit information. Neutral atoms, analogous to captured ions, are available in a variety of different species and quantum states, providing a rich and identical choice of physical quantum bits with a rich set of internal quantum states. The different choices of atoms and quantum states are largely determined by trade-offs between well-isolated states with long coherence times and accessible quantum levels that are easy to initialize, manipulate, detect, and implement quantum gates.

Early experiments with heavy base atoms such as rubidium and cesium atoms were studied with the help of laser cooling and optical or magnetic trapping techniques. Because of their long coherence times and large level spacing up to GHz, superbase states can be used to encode quantum bits. Moreover, they can be easily initialized and detected by techniques such as optical pumping. Recently, more atomic species have been investigated and new possibilities for the operation of more highly inert quantum bits have been demonstrated. Alkaline earth atoms with two valence electrons (e.g., strontium) can be further cooled by narrow-line cooling in an optical trap, leading to further super-forcing decoherence induced by atomic motion. Single-photon excitations from the ground state to the Rydberg level typically have higher excitation Rabi frequencies than two-photon Rydberg excitations of alkaline atoms at similar laser powers.

Long coherence times for physical quantum bits are one of the fundamental requirements for quantum computing. More than 10^4 quantum gates are required in the coherence time to reach the QEC threshold . The mechanism by which the super-sinusoidal coherence of captured atoms occurs has been analyzed in detail by Kuhr (et al.). Under normal conditions, the atomic loss rate is mainly due to collisions with the background gas and atomic heating; with proper shielding from radio frequency (RF) noise, the longitudinal relaxation time is limited by Raman scattering, which can be suppressed by placing the atoms at the intensity minimum of the blue detuned optical trap.

The transverse relaxation time is affected by a range of phase-dissipating mechanisms: including fluctuations in the magnetic field, and fluctuations in the trap depth and position, while the thermal motion of the atoms can be suppressed by cooling the atoms down to a kinematic ground state. Similar techniques can also be used to balance the coherence time of mixed isotopes and further extend the coherence time to close to 1 second.

When building a two-qubit quantum gate, Rydberg excitation or trimming is used, which also requires a longer coherence time. The main reason for decoherence comes from inert lifetimes due to spontaneous radiation and BBR-induced jumps. Coherence times of up to 27 μ were demonstrated experimentally due to the reduction of the laser phase noise and the implementation of the spin-echo protocol. The decay due to the spontaneous emission of intermediate states can be reduced by increasing the laser power, increasing the intermediate state detuning, or employing a single-photon excitation scheme.

2) Scalability of neutral atom systems

Neutral atom quantum computing platform. (a) The platform consists of a classical computer and a quantum processor based on neutral atoms. The latter consists of an array of atoms in a vacuum chamber, peripheral devices for detecting and controlling the atoms (e.g., laser/microwave resources, optical/microwave modulators, cameras, and corresponding control electronics). (b) General overview of the neutral atom quantum computing architecture. At the physical level, the neutral atoms in the quantum processor are first cooled and trapped by a magnetic optical trap (MOT) in an ultra-high vacuum chamber. The atoms are then loaded into an array of optical tweezers or an optical lattice, where they are initialized with optical pumping, followed by control of a sequence of quantum gates by laser and microwave ion beams. Finally, the quantum information is read out by fluorescence imaging. The combination of noisy physical quantum bits with open-loop quantum control techniques such as dynamic decoupling builds virtual quantum bits with higher effective coherence time and minimum system gate error, which can be used as the basic building blocks for general-purpose quantum computation based on quantum error correction or for noisy medium-scale quantum applications. At the logic and QEC layers, the quantum circuit decomposition of quantum algorithms and the data processing of the detection results are handled by classical computers. The user interface at the application layer is also handled with the assistance of a classical computer.

Scalability is one of the core challenges in realizing large-scale quantum computing. As a rough estimate, the number of physical quantum bits required for a rudimentary general-purpose quantum computer can easily exceed 10^6. To run a quantum algorithm with a predetermined circuit depth of 10^10, highly noisy physical quantum bits with an actual error rate of 10^(-4) will likely seek the help of QEC. Since thousands of physical quantum bits are typically required to compose a logical quantum bit, a quantum algorithm with a few hundred log quantum bits could easily turn out to require approximately millions of physical quantum bits.

From this perspective, neutral atoms may be the most promising platform for building QEC codes, as there are only weak magnetic dipole-dipole and vdW interactions between ground-state atoms, which makes it possible to massively tightly trap many atoms with the richness of configurations demonstrated by optical tweezers arrays or magnetic trapping arrays.

Neutral atoms are essentially identical, so the need for physical resources such as laser frequencies does not increase with the expansion of quantum bits. However, neutral atom-based systems can suffer from crosstalk if single-point addressing is not fully satisfied during gate operation or if spontaneous radiation from an image atom is reabsorbed by nearby atoms during quantum bit measurements.

The most challenging issue for neutral atom-based QC platforms is the randomness of atom loading into individual traps. Collisional blocking limits the probability of loading a single atom into a small volume trap to about 50%. A possible approach to increase the loading probability is to increase the loading probability by using blue detuned catalytic light or by using superfluid-mott insulator transitions in optical lattices, but with longer experimental cycles.

3) Initialization and state detection in computation

Initialization and state detection in computational networks usually involve dissipative processes. Initialization of the ground state quantum bits can be simply achieved by optical pumping. To encode a quantum bit into a known pseudo-state, an additional step of coherent pop transfer is required.

State measurements are a key element in quantum formation readout as well as measurement-based quality control or error correction. A simple way to measure atomic states is to push out all the atoms of one state by resonance and then detect another state by resonance fluorescence imaging of the remaining atoms. This destructive measurement has an error rate as high as 0.9997, but is unable to distinguish between atoms that are selectively pushed out and those that are lost due to background collisions. In addition, the probability of losing about half of the atoms means that atoms need to be replenished after each measurement, which significantly increases the cycle time of the calculation.

To address these issues, scientists have developed in situ NDT techniques based on state-selective fluorescence for optical lattice and optical tweezer systems. Unlike non-destructive measurements, which are often mentioned in quantum computing, non-destructive measurements are measurements in which a quantum bit state is projected into the same Hilbert space formed by the base state of the quantum bit without excitation to other atomic layers, "non-destructive measurements" are measurements in which the quantum bit state is projected into the same Non-destructive measurements" are measurements in which quantum bit states are projected into the same Hilbert space formed by the base states of the quantum bits without excitation into other atomic layers.

"Non-destructive" measurements here emphasize measurements without loss of atoms, since atoms exiting to other levels can be easily reinitialized by optical pumping. A great deal of effort has gone into the trade-off between higher contrast over more imaging cycles to counteract the dark noise produced by non-ideal photon detectors, and the resulting loss of atoms due to heating. Optimal results require the use of collecting lenses with moderately high numerical apertures, deeper optical traps, and careful preparation of the polarization state for the probe lamp.

Detection of atomic states by spatially resolved imaging. (a) Left: fluorescence image of atoms in mutually independent one-dimensional spin chains. (b) Right: spin-resolved detection. Atoms with different spin states are separated by applying a magnetic field gradient and their wave functions are projected to one of the two sites of the double-well potential after spatially resolved imaging. (b) Left: fluorescence imaging of a 3D optical lattice one layer perfectly filled after classification of a random half-filled lattice. (c) Right: atoms with different quantum bit states are separated by a state-dependent optical lattice, and after spatially resolved imaging, their wavefunctions are projected onto one of the two lattice sites. The yellow dashed lattice and square pattern indicate the initial position and occupancy map of the atoms, respectively.

At the heart of both digital and quantum computers are logic gates. Quantum computers work on the atomic scale, where quantum mechanics dominates, which means that logic gates must also be built from atoms. For example, a NOT logic gate has only one input and two states: i.e., 0 and 1.But for a logic gate to work, the atoms must not only interact with each other, but also control the interaction. The electric dipole strength of Rydberg atoms and our ability to control their excitations make them perfect for quantum logic gates.

In 2010, Saffman and his colleagues in Wisconsin demonstrated the ability to build logic gates using two neutral rubidium atoms, complementing work done by a team led by Philippe Grangier at the Institute of Optics near Paris. The quantum version of NOT logic gates are controlled-NOT logic gates (or CNOT logic gates), in which the rubidium atoms themselves are quantum bits of information. One is labeled "control" and the other is labeled "target". In their ground states, there are various hyperfine states, which hold quantum information, and there is no interaction between the atoms: the four-micron distance between them is like an infinity. However, by emitting resonant photons at the control atom, exciting it to the Rydberg state, and absorbing it, the valence electrons rise to a higher energy level, expanding their reach enough to interact with the target atom, "flipping" it, and allowing the CNOT gate to operate.

Previous experiments have used ions to create CNOT logic gates, but the problem with ions is that there is no easy way to turn off their interactions due to their charge, which limits how many ions can be combined into a stable quantum bit. Neutral Rydberg atoms, on the other hand, do not have this problem. This is not to say that Rydberg atoms are a new development: their existence was known as early as the late 19th century.

(a) and (b) show level diagrams for single quantum bit operations in the case of a ground state manifold and the inclusion of a Rydberg state, respectively.

Pulse sequence of a controlled phase gate with Rydberg blockade. (a) and (b) show the dynamics of the ground state |01〉 and |11〉, respectively.

Performance of quantum gates and their implementations. Figures (a), (b) and (c) show the configuration, initialization inertia and truth table inertia of a two-qubit C-NOT gate, respectively. Figures (d), (e) and (f) show the configuration, initialization and truth table of the three-qubit Tofoli gate, respectively.

What really pushed Rydberg physics forward was the advent of laser trapping and cooling techniques, for which Steven Chu, Claude Cohen-Tannoudji and William D. Phillips shared the Nobel Prize for Physics in 1997. It was this ability of physicists to utilize light to capture and manipulate individual atoms that opened the way for strange new applications of the Rydberg atom.

Despite the steady increase in the number of atomic quantum bits and the realization of quantum gate inertia in state-of-the-art experiments, the realization of general-purpose quantum computation using QECs remains a long-term goal that is difficult to achieve even with amplified systems based on existing platforms. However, at the NISQ level, neutral atom-based systems can still accomplish some complex computational tasks and exhibit certain quantum properties and advantages.

One of the recent applications of neutral atom-based platforms is to solve complex optimization problems by measuring the initial state of time-evolving quantum many-body systems. A promising paradigm for achieving this goal is the quantum annealing algorithm (QAA), which obtains a solution to the problem by adiabatically driving the system to converge to the instantaneous ground state of the target Hamiltonian.In 2013, Keating et al. proposed a quantum annealing algorithm based on Rydberg atoms, which can be used to solve quadratic unconstrained binary optimization problems. Later, Glaetzle et al. proposed a generalized quantum annealer with all-pair-all coupling using Rydberg-mediated four-body interactions. Subsequently, it was found that the anisotropy of the Rydberg interactions also facilitates the construction of different universal annealers. In addition to QAA, hybrid quantum classical variational methods such as the quantum approximation optimization algorithm (QAOA) can also be implemented in Rydberg atomic systems. Recently, it has been found that two-dimensional neutral atomic systems are suitable for solving the QAOA-based maximum independent set problem and the MaxCut problem.

Controllable large-scale quantum systems not only have the potential to build general-purpose quantum computers, but are also ideal for building quantum simulators. The aim of quantum simulation is to use synchronized quantum systems to simulate real-world model Hamiltonian-based many-body physics problems, which are generally difficult for classical computers to solve due to the exponential growth in the size of the Hilbert space as the number of particles increases.

In recent years, great success has been achieved in simulating many-body physics on various platforms, among which neutral atomic systems with Rydberg interactions seem to be a promising choice. In Rydberg atomic systems, strong and tunable interactions combined with available coherent control and dissipation management make it possible to simulate a variety of many-body problems: e.g., coherent spin model simulations, many-body molecular dynamics, and drive-dissipation systems.

1) Coherent spin modeling

One of the most important research directions in Rydberg's atomic many-body systems is the simulation of coherent spin models. For this purpose, atoms are first loaded into a given lattice configuration (or set) and prepared according to a specific initial state. Subsequently, the system evolves coherently driven by the Rydberg interaction, during which the degrees of freedom of motion of each atom can be considered "frozen" if the evolution time is very short. In this frozen-gas limit, the dynamics changes only the internal atomic states, thus effectively modeling the interacting spin system.

(a) Left: phase diagram of the ground state of the Rydberg Ising chain. Right: adiabatic preparation of ordered ground states of 12-atom chains driven by quantum phase transitions at different values of the interaction range Rb /a. (b) Left panel: realization of topological and trivial staggered chain configurations for the SSH model. (c) Right: site-resolved single-particle eigenstate excitation spectra probed with detuned Δμw driven by a weak microwave field.

2) Dynamics of atomic and electronic motion

In a more realistic context, by considering atomic and electronic center-of-mass motions, the Rydberg atom has the potential to help us gain insight into many-body physics on a broader scale.

First, applying Rydberg atoms to a collection of ground state atoms can enrich the properties of ultracold quantum gases. When an atom is deeply trapped in a potential well, it cannot jump to a nearby lattice site. In this case, distance-dependent Rydberg interactions change the vibrational state of the atom in the trap, resulting in effective phonon dynamics.

Excitation of atoms to the Rydberg state by ultrashort coherent laser pulses provides a way to explore many-body physics of strongly interacting electrons. In this ultrafast quantum simulator, many Rydberg electrons are excited into orbitals far from the cation core. As a result, the wave functions of these electrons spatially overlap with each other, resulting in strong many-body correlations induced by Coulomb interactions. Based on this idea, Takei et al. observed coherent many-body electron dynamics in a collection of atoms by time-domain Ramsey interferometry. Subsequently, Mizoguchi et al. investigated the many-electron dynamics of anatomical Mott insulators in optical lattices. As they observed experimentally, the overlap of nearby Rydberg electron wavefunctions leads to a sharp change in the ion counting statistics and a sharp increase in avalanche ionization, thus opening the way to the study of the metal-like phase of the Rydberg gas.

(a) Simulation of a Hubbard model with Rydberg-modified ground state atoms in a light lattice. Here, U1 and U2 denote the Rydberg modification-induced nearest-neighbor and next-nearest-neighbor interactions, respectively, and t denotes the tunneling rate between neighboring sites. (b) Rydberg interactions induce photon exchange between two atoms in a deep optical trap. (c) Left panel: radial wave functions of Rydberg electrons in neighboring lattice sites at different principle quantum numbers. (d) Right: Rydberg excitation and ion probing scheme for studying many-body electron dynamics.

3) Many-body physics of dissipative systems

In realistic Rydberg atomic systems, the coherent driving of external electric fields often competes with dissipation due to environmental coupling. Such controllably driven dissipative systems with strong nonlocal Rydberg interactions can be used to model many-body phenomena different from fully coherent ones, such as dynamical phase transitions far from equilibrium.

(a) Illustration of promotion kinetics, where V (0, T) in the left panel denotes the vdW interaction between a Rydberg atom located at the origin and another Rydberg atom located at a distance T from the origin. The right panel indicates promotion-induced aggregation. (b) Evolution of the density of the remaining atoms in the gas driving the dissipative Rydberg at different initial densities above and below threshold. Above threshold, the total density of remaining atoms is attracted to the same steady-state value, while the dynamics becomes stable at initial densities below threshold. The corresponding self-organization process is depicted in the inset, where the blue dots and red balls represent atoms in the ground state and Rydberg state, respectively.

The above article focuses on quantum information processing (QIP) with neutral atoms as physical quantum bits. In another direction, the combination of Rydberg atoms and photons opens an avenue for studying photonic quantum computation and quantum simulation: as optical quantum bits, individual photons can be easily manipulated and transported over long distances, which makes them natural information carriers for quantum communication and quantum networks.

(a) Level diagram of the four-wave mixing scheme used for single-photon generation. (b) Experimental setup and measured two-photon correlation function. (c) Level scheme of the Rydberg EIT. (d) Schematic of the Rydberg EIT configuration and measurements of probe photon transmission at different intensities. (e) Two-photon correlation function for transmission of probe photons in a resonant Rydberg-EIT configuration.

Controlling photons with photons requires a nonlinear medium. Conventional materials have relatively small nonlinearities at the level of a few photons, so a large number of photons are usually required to observe nonlinear optical effects. Quantum nonlinear optics opens the door to studying the mechanisms by which a single photon can significantly affect the state of another photon - a strong nonlinearity that is key to all-light quantum logic operations.

(a) and (b) show the level schemes for realizing the control and target quantum bits of a photonic quantum gate, respectively. When both photons are in the left circularly polarized state |L〉, the total wave function will pick up an interaction-induced phase. (c) and (d) show the measured truth table for the C-NOT gate.

Rydberg-mediated photon interactions not only provide support for the construction of quantum logic operations, but also facilitate quantum simulations with photons.

Indeed, the simulation of oligomeric dynamics with interacting photons has attracted much attention. Particular attention has been paid to photonic molecules - bound states formed by a few photons, which are analogous to molecular states formed by the binding of massive particles under attractive interactions. In an atomic environment, the Rydberg EIT with large intermediate states detuned by Δ gives the photons attractive forces and effective mass, which opens the door to the existence of photonic bound states.

Quantum many-body physics is at the heart of quantum simulations. Many-body physics of interacting photons is particularly interesting because the nonlocal nature of photons can give rise to phenomena that have no counterpart in other platforms. A prominent example is the prediction that photons traveling through a collection of Rydberg atoms can form moving frame crystals. There are many experiments exploring this multi-photon scattering mechanism: including interactions between many photons and a Rydberg superatom, single-photon sub-traction mediated by many-body decoherence, and photon transport through a collection of dissipative Rydberg atoms at large input rates ......

Theoretical treatments of multiphoton scattering in a collection of Rydberg atoms are quite difficult, and several methods have been developed to reveal the underlying many-body dynamics.In 2013, Gorshkov, Nath, and Pohl introduced a time-ordering method for describing the scattering of short pulses in a dissipative Rydberg medium and demonstrated that the output single-photon is impure. Since then, this method has been generalized to the continuous-wave limit with linear EIT losses, and to the case with arbitrary scattering coefficients.In 2016, Gullans et al. developed an effective field theory to describe many-body dynamics in dispersive Rydberg media, and numerical methods such as matrix primitives have been applied to the calculation of scattering dynamics.

(a) and (b) show the experimental setup for observing two-photon bound states and the measured two-photon correlation function, respectively. (c) and (d) show the experimental setup for observing three-photon bound states and the measured three-photon correlation function, respectively.

The above article briefly summarizes the basic working mechanisms and state of the art of quantum computation and quantum simulation based on Rydberg atoms, with special emphasis on several recent experimental advances made in this field over the past few years: e.g., the preparation of large-scale arrays of defect-free atoms, the realization of high-fidelity quantum gates, the simulation of the quantum spin model, and the demonstration of single-photon-level optical nonlinearities, to name just a few. These achievements pave the way for continued success in quantum spin research based on Rydberg atoms and hold exciting prospects for the development of scalable quantum computation and simulations in the coming decades.

For neutral atom-based quantum computation and simulation, an important future direction is to improve the inertia of quantum state manipulation. To this end, more emphasis should be placed on upgrading current experimental techniques, such as checking and minimizing errors, the trapping of Rydberg atoms, and the application of cyclic Rydberg states. With continued improvements in inertia, coupled with continued efforts to scale up quantum bit arrays, we will be able to realize Rydberg quantum computers/simulators that will outperform the best classified computers for certain computational tasks.

When it comes to quantum computers, Rydberg physics is not the only way to realize them. Ion traps, superconductors, diamond and Bose-Einstein condensates are all contenders for the quantum "holy grail". However, Rydberg atoms have other uses. For example, by selecting a cluster of Rydberg atoms at a particular resonance frequency (e.g., terahertz or microwave), it can act as a sophisticated sensor that produces light output when it receives these fields; photon-photon interactions in the presence of a Rydberg blockade may even lead to exotic light states thought to be crystals or liquids, where the interactions bring photons together to look like a "light saber". a "lightsaber".

In addition to quantum computing, neutral atom systems with Rydberg interactions can also be used to prepare highly entangled states, such as the recent generation of 20-qubit GHZ states by a quasi-adiabatic drive at an efficiency of 50 billion times. In the near future, it will be possible to continuously increase the entanglement and scale of highly nonclassical states by means of diabatic drives, Rydberg dressing, dissipation-assisted evolution, quantum cellular automata paradigms, or variational methods.

At the same time, the application of these entangled states to Rydberg-based precision measurements, such as probing weak or microwave electric fields to improve detection sensitivity, is also a promising direction.

"Over the past decade, Rydberg physics has gained momentum." Charles Adams, a physicist at the Joint Quantum Center at the University of Durham in the UK, has said, "There are research groups doing work in this area almost everywhere now. Considering that the ingredients of Rydberg physics are some of the simplest things in the universe: atoms and photons, it's remarkable what it can achieve."

Reference Links:

[1]https://physicsworld.com/a/the-rise-of-rydberg-physics/

[2]https://cpb.iphy.ac.cn/EN/10.1088/1674-1056/abd76f

[3]https://mp.weixin.qq.com/s/NDwrVMH8P5EmPMl-nBdbTw