The quantum volatility, macroscopic quantum coherence and artificially controllable nature of the cold atom system make it a completely new quantum system, and its novel quantum state and exotic physical properties are the foresighted and challenging frontier fields in the world. Since the realization of thin gas Bose-Einstein condensation in 1995, the study of one-component and simple interactions has gradually transitioned to the study of multi-component, complex multibody effects, and new physics such as spin-orbit coupling, non-ermi, strong correlation, and disorder effect. The article introduces the research progress of cold atoms in recent years, including the related technologies of cold atoms, the important work of cold atoms in quantum precision measurement, quantum simulation and quantum computing, and hopes to give new enlightenment to future research.
Written by | Yihui Xing, Wentong Li, Wuming Liu (Institute of Physics, Chinese Academy of Sciences)
Source | This article is from Physics, No. 2, 2022
01
introduction
In microphysics, temperature is a measure of how intensely an atom does irregular thermal motion: the higher the temperature, the faster the rate of motion of the atom and the more intense the thermal motion; the lower the temperature, the slower the rate of motion of the atom, and the weaker the thermal motion. This irregular thermal motion is difficult to predict and manipulate, and often introduces errors in the course of experiments. It is conceivable that if the intensity of the thermal motion of the atom can be reduced as much as possible, that is, the temperature can be reduced as much as possible, the experiment will be greatly optimized, and this field of research is collectively referred to as cold atom physics.
Cold atoms have the following two characteristics: first, the cold atoms have a slow rate of motion and few collisions with each other, making them easy to manipulate while also reducing the spread of the energy spectrum, which helps to improve the measurement accuracy; second, the de Broglie wavelength of the cold atom is very long, showing obvious quantum characteristics, has strong coherence, and can produce macroscopic quantum effects, one of the most important representatives is the Bose-Einstein condensed state (BEC), in which all bosons are in the lowest energy ground state. Based on these two excellent characteristics, cold atom physics has a wide range of applications in many fields such as quantum precision measurement, quantum simulation, and quantum computing. High-precision absolute gravity meter based on atomic interference can measure changes in gravity field for seismic monitoring and groundwater detection, more accurate atomic clocks provide a strong guarantee for global positioning and communication systems, quantum memory and quantum chips made of cold atoms will be the basic components of quantum computers, highly controllable and pure cold atomic systems for the Hubbard model, Su-Schrieffer-Heeger (SSH) Simulations of quantum systems such as models provide an ideal experimental platform.
02
Cold atom technology
In 1975, H NSCH and Schawlow proposed a method of laser cooling[1], the basic principle of which is to use the scattering between photons and atoms to reduce the rate of motion of atoms, so as to achieve the effect of cooling. When an atom collides with a photon moving in opposite directions, the atom absorbs and transitions the photon to the excited state, and due to conservation of momentum, the atom will continue to move forward at a slower rate than before, and then spontaneously transition back to the ground state at some point, randomly releasing a photon in one direction. If this process is repeated in large quantities, the recoil effect of the photons emitted in all directions on the atoms will cancel each other out, and eventually manifest as the atoms slowing down in the original direction.
Laser cooling can obtain extremely low temperatures, opening a door for people to study the physics of cold atoms. In 1982, Phillips et al. achieved laser cooling of neutral sodium atoms for the first time[2], reducing the rate of sodium atoms to 4% of their original rate, equivalent to reducing the temperature to 70 mK. Just three years later, Chu et al. cooled the sodium atoms further to 240 μK[3], reaching the limit of Doppler cooling. After that, methods such as polarization gradient laser cooling and velocity selection coherent particle number captive cooling have broken through the Doppler cooling limit. Today, the temperature of pK levels can be obtained in the laboratory, which is gradually approaching absolute zero, and the cooling of almost all alkali metal atoms and some alkaline soil and rare earth atoms has been achieved. In addition to atoms, cooling of molecules [4] and ions is also gradually realized. Langin et al. obtained ultracold neutral plasmas by photoionizing ultracold neutral atomic gases[5] at temperatures of 50 mK, breaking the limitations of traditional high-temperature plasmas and deepening the study of neutral plasmas into the strongly coupled region. Even laser cooling studies have been conducted on antimatter. In 2021, Baker et al. performed one-dimensional laser cooling of an antihydrogen atom composed of an antiproton and an antielectron for the first time[6], observing a 1s-2s transition spectrum narrower than that of an uncooled antihydrogen atom (Figure 1), a result that will facilitate ongoing spectral and gravitational studies of antihydrogen atoms and open up new approaches for future antimatter experiments.
Fig. 1 Cooled antihydrogen atoms have a narrower 1s-2s transition spectrum than uncooled antihydrogen atoms[6]
Another method developed at the same time as laser cooling is evaporative cooling, the specific process is to achieve equilibrium in the rate distribution in the atomic group, the atoms with larger rates are eliminated, and the remaining atoms will reach a new equilibrium in the collision, when the rate of atoms will be reduced in general, which can further reduce the temperature, which plays an important role in the acquisition of BEC. In addition, Gisbert et al. discovered a collaborative cooling mechanism caused by the exchange of photons between atoms when studying one-dimensional cold atomic chains[7], which can reduce the spontaneous radiation of atoms when the chain is long enough to make the chain more stable, and the analysis also shows that this effect may be more pronounced in the two-dimensional situation.
The atom is in motion all the time, and in order to prevent the atom from running around, it needs to be captured in a potential trap. Using the interference between the reverse laser beams, a stable array of periodic optical potential wells can be formed in space, and the captured atoms are arranged in an orderly manner in these optical potential traps, similar to the crystal structure, so it is called a photolattice. By designing parameters such as the direction, wavelength and potential well depth of the laser beam, various lattice structures can be obtained and the transition of atoms between different lattice points can be controlled. In 2016, Endres et al. used 100 optical tweezers to assemble more than 50 atoms one by one into defect-free one-dimensional arrays in less than 400 ms [8]. An optically compensated zoom lens designed by Lee Jae Hoon et al.[9] can produce an optical dipole trap for transporting cold atoms, which has the advantages of high accuracy, constant potential well depth, long moving distance, and easy configuration, which can complement the assembly method of the optical lattice. The assembly of three-dimensional optical lattice is difficult, especially the three-dimensional lattice with different shapes or stacking methods between layers, such as twisted double layer graphene. Therefore, Hao Lei proposed a scheme for assembling a three-dimensional optical lattice layer by layer [10], first using a laser beam splitter to obtain a multi-layer two-dimensional optical lattice, and then using a beam shaper composed of two cylindrical thin lenses to compress the laser beam in the z direction, so that the distance between the layers becomes smaller, you can get a three-dimensional optical lattice, and you can achieve relative slippage between different layers by controlling phase parameters, and achieve relative torsion between different layers by rotating the mirror on the x-y plane. This scheme has a good application prospect in the study of complex lattice structures.
By analyzing the light images refracted or absorbed by the cold atomic system, it is possible to extract physical information about the atomic system synthesis. Common imaging techniques include absorption, fluorescence, and phase contrast, as well as out-of-resonance out-of-focus imaging (ORDI) [11]. For ions in cold atomic gas, Gross et al. proposed a method for imaging using ion-Reedberg atomic interaction-induced absorption [12] to image the dynamic evolution of ions in a time-resolved manner.
03
Quantum precision measurement
Quantum precision measurement is one of the important applications of cold atoms, and its main task is to continuously improve the accuracy of measurements. Usually we have two means to improve the measurement accuracy, the most direct way is to find the smallest scale of the "ruler", for example, the minimum scale of one meter of the ruler can not measure the length of a few centimeters, but the minimum scale is a centimeter of the ruler can measure the length of several centimeters; the other way is to make multiple measurements, the use of statistical laws to reduce the error generated by each measurement, the mathematical central limit theorem tells us that the same amount of N independent repetition of the measurement, all the results obtained obey the normal distribution, The error of each measurement is the measured value
, known as the shot noise limit, is the highest accuracy that classical measurement methods can theoretically achieve.
With the continuous development of quantum technology, it has been found that if the unique properties of quantum mechanics, such as coherence and entanglement, can be used in the measurement, the limitation of the classical bulk noise limit can be broken and the accuracy of the measurement can be further improved. If the quantum states of the N detector particles are entangled with each other, the external effects on these N particles will be coherent and superimposed, and the final error will be measured
, which improves the allowable accuracy over the classical shot noise limit
times, called the Heisenberg limit. This is the measurement error caused by Heisenberg's uncertainty principle, which comes from the quantum fluctuations in the vacuum and cannot be eliminated, in other words, the Heisenberg limit is the highest precision that the quantum measurement method can theoretically achieve.
Although ideal quantum measurement methods can achieve high precision, it is extremely difficult to entangle N particles and is actually difficult to achieve. The research task of quantum precision measurement is to break through the limit of shot noise and constantly approach the Heisenberg limit. Due to the long de Broglie wavelength of cold atoms, it is very easy to exhibit quantum properties, so it is suitable as a tool for quantum precision measurements. The following will introduce the progress in recent years in the process of approaching the Heisenberg limit in three aspects.
3.1 Quantum measurements using compressed states
Heisenberg's uncertainty limits the overall accuracy we get when measuring multiple physical quantities at the same time, and if we relax the accuracy requirements for one of them, we can make the other physical quantity more accurate, this quantum state is called the compressed state. Hosten et al. calculated the noise level based on experiments with optical cavity measurements of clock-state rubidium atoms[13], and in the absence of entanglement, the error can be expressed as
N is the number of atoms, by "compressing" the quantum state in the degrees of spin freedom, that is, entanglement is generated, as shown in Figure 2, the uncertainty of the quantum state in the y and z directions is the same when uncompressed, the uncertainty in the y direction after compression increases, and the uncertainty in the z direction decreases, and the measurement error in the z direction is obtained by using the compressed state again, which can be obtained by calculation
Where α is a parameter determined by the shape of the atomic cloud and laser beam, due to α 1, it can be seen that the measurement error in the presence of entanglement is much smaller than without entanglement, meaning that the classical shot noise limit is exceeded.
Figure 2 (a) Representation of uncompressed spin quantum states on Bloch spheres, with spots representing uncertainty, the same uncertainty in the y and z directions when uncompressed; (b) the probability distribution of uncompressed quantum states in the z direction; (c) the expected value of error when using uncompressed states; (d) the representation of compressed spin quantum states on the Bloch sphere, with increased uncertainty in the y direction and decreased uncertainty in the z direction; (e) blue for the probability distribution of the uncompressed state, red and yellow for (d) Probability distribution of two compressed states in a plot[13]
In 2020, Szigeti et al. proposed that the atomic interactions inherent in BECs would improve the accuracy of measurements, based on research on cold atom gravimeters[14]. The Hamiltonian amount of the system is
3.2 Combined with weak measurements
In quantum mechanics, the measurement process is actually the process of coupling the instrument to the quantum system, the result of the measurement is to project the quantum state of the system to the eigenvalue of a certain eigenstat, and after the measurement, the wave function of the system collapses to this eigenstat, so that the state of the system can not return to the original state, and it cannot be repeatedly measured, which is what we are familiar with as strong measurement. In 1988, Aharonov proposed the concept of weak measurements, making the coupling of the instrument to the quantum system very weak, only extracted from the system
Reached the Heisenberg limit. About 100,000 photons were used in the experiment, which improved the accuracy by two orders of magnitude compared to classical measurement methods. This is the first time in the world that the Heisenberg limit has been reached in actual measurements and can be achieved without the use of entanglement.
Fig. 3 The relationship between the measurement accuracy and the number of photons, the point in the figure is the result of selecting a specific set of parameters, the blue line is the fit to the point, and the purple line is the boundary of the mixed state measurement accuracy[15]
Fig. 4 Measurement error of three parameters. The solid and dashed lines in the figure represent the minimum theoretical error, and the points represent the experimental measurement results, which can be seen that the three parameters in the experiment have reached the minimum error at the same time. where the curve is a classical independent measurement, an entanglement independent measurement, a entanglement joint measurement, and a control enhancement sequence measurement[16]
3.3 Optimal solution for multi-parameter measurement
In the actual measurement, it is often necessary to measure multiple parameters at the same time, according to the Heisenberg uncertainty principle, if two parameters are not easy, it is impossible to accurately measure them at the same time, the previously mentioned compression state is to discard the accuracy of one of the parameters in exchange for the higher accuracy of the other parameter. So, how to take into account multiple parameters at the same time to make the best measurement?
Figure 5 The mean squared error of the parameter estimation using coherent states for the real and imaginary parts of the complex α is prohibited by the uncertainty principle in the lower left region of the curve. The solid black line represents the constraint relationship; the red dotted line represents the geometric mean quantum measurement limit based on the right logarithmic derivative; the blue dotted line represents the arithmetic mean quantum measurement limit based on the right logarithmic derivative; and the green dot line represents the harmonic mean quantum measurement limit based on the symmetrical log derivative[17]
04
Quantum simulation
Thanks to advances in atomic control technology, cold atoms became an idealized platform for quantum simulations [18, 19]. We chose the following 4 themes to demonstrate the simulation power of cold atoms. One is the cold atom simulated spin-orbital coupling (SOC), which also includes the coupling between the recently proposed centroid orbital angular momentum and the spin, that is, the spin-orbit-angular momentum coupling (SOAMC). The second is that in recent years, the field of condensed matter physics has been widely studied in the field of physical phases, such as supersolid and topological phases, the system is described by the Hamiltonian quantity including SOC and Hubbard terms, and under the competition of these interactions, the physical system can exhibit strange phase transition behavior. The third is that cold atoms simulate non-Ermi quantum systems, focusing on analyzing their behavior different from those of Ermi systems. The fourth is that unlike the previous analysis on flat Riemann manifolds, new physical images of BEC phenomena are given on hyperbolic manifolds.
Of course, the simulation power of cold atoms is far more powerful than this, and many interesting physics systems are not included in these topics, such as simulating nonlinear systems[20] and dissipative systems.[21]
4.1 Spin-orbit coupling
Spin-orbit coupling (SOC), in which ultrafine spins inside an atom are coupled to atomic mass cardiacs through a two-photon Raman process,[22-24] are equivalent to being subjected to SU(2) non-Abelian canonical potentials,[25] and can produce many interesting physical effects [26,27]. Recently, new phenomena of angular momentum and ultra-fine spin coupling of atomic centroid orbits have been discovered[28] and can be achieved in a spin BEC with two Laguere-Gaussian lasers [29,30].
Fig. 6 Fermi atoms with 1/2 spin and Raman laser action (a) Two beams of homogeneous propagation with different orbital angular momentum (-l1 and -l2) Gaussian laser-atom-induced SOAMCs; (b) Schematic diagram of energy level transitions; (c) Polyselectronic diagram of Fermi superflows of two-dimensional SOAMCs in the plane of Ω0-δ, other parameters set to l= 3, EB/EF= 0.5. Supercurrent state (SF), normal normal (N), vortex state with energy gap (V1), and vortex state with no energy gap (V2) are included[31]
Consider a two-component spin 1/2 fermi gas confined to the x-y plane, coupled to two Raman laser beams with different orbital angular momentum (Figures 6(a), (b)). A monogram transform yields the effective Hamiltonian quantity of a single particle in a polar coordinate system[31]:
It can be seen that many other novel physical phases can be discovered using high-spin SOCs or SOAMC, which makes it a "technical means" that combines with various models to obtain richer physical images such as supersolid (SS), superradial [33], topological states, etc.
4.2 Quantum phases
Supersolids are both superfluids with non-diagonal long programs and solids with diagonal sequences, and the concept was first proposed in solids 4He .[34] As a novel state of matter, its realization method has always been the goal of theoretical and experimental pursuit. There are many theoretical ways to predict that supersolids can be achieved, such as applying SOCs in one- or two-dimensional spin-volume BEC systems [35,36], dipole Fermi systems, etc.
Considering two-dimensional Bose gases with SOC and soft-core long-range interactions in the literature [35], Hamiltonian quantities under the Gross-Pitaevskii average field approximation can be written as:
The multibody ground state is obtained by minimizing the Hamiltonian amount by the virtual time algorithm value, as shown in Figure 8, when the parameters are fixed, the vortex circulation direction is the same, showing a periodic vortex arrangement, which is supersolid. Components with weaker interaction intensity at the same time form the central part of the vortex and are surrounded by components with strong interactions. When the intensity ratio of the exchange interaction, the direction of the vortex circulation changes, and different components are exchanged and distributed, so this super-solid is called the hand sign super-solid. When the interaction intensity ratio continues to be changed, other supersolid phases will also appear, such as planar wave supersolic, standing wave supersolid, spin polarized supercurrent phase, etc.
Cold atoms in periodic optical potential wells can occupy only a small number of low-energy Bloch bands, and the interaction between cold atoms in the same potential well is large, allowing for good simulations of strongly correlated lattice models, such as the Hubbard model [38,39]. At the same time, the Hubbard model can produce many novel topological states, making the Hubbard model a boom in research. The literature [40] indicates that a two-dimensional Hubbard-Hofstadter model can be simulated using a cold atom system in a photolattice, where the Hubbard term is treated similarly to the BCS average field approximation. The presence of majorana-Kramers pairs (MKPs) was discovered to support the discovery of higher-order topological phenomena. The same literature [41] also shows that a first-order (with zero-energy edge state) and a second-order (with zero-energy angular state) topological superconducting phases are obtained in a two-dimensional extended Hubbard model with two SOCs, Rashba and Dresselhaus, and that changing the temperature or chemical potential can effectively regulate this phase transition.
4.3 Non-Ermi
With the gradual deepening of research, the study of quantum systems has moved from closed systems to open systems, that is, non-Ermi systems, showing its unique physical effects, such as singular points (EPs)[42] and non-Ermi skin effects [43]. Cold atoms in optical systems, however, can well simulate non-Ermi effects due to their maneuverability [44-46].
In the literature [47], it is proposed that the transition term in the Hamilton quantity can be realized by using the cold atom two-photon Raman auxiliary transition, and the atomic resonance is transferred by the radio frequency pulse to obtain the loss term, thereby obtaining a non-ermi three-dimensional continuous Hamilton amount:
Calculate the energy spectrum of non-Ermi, it is found that there is also a topological phase in the high-dimensional system, and at the same time, unlike the Ermi case, the zero-energy surface mode of the non-Ermi system is regulated by the lattice size: because the degree of localization of the surface mold is not high, when the number of lattice points N is too small, the zero-energy mode is not strictly localized at the edge, so the surface mold disappears, but the enhancement of the non-Ermi strength, that is, increasing γz, can make the surface mold reappear. In addition, changing the momentum can adjust the position of the center of the surface mold local area.
The body-edge correspondence of the non-Ermi system is described by the non-Bloch theory, from which the integral interval for calculating the topological invariants is not the Brillouin region of the Ermiean case, but the generalized Brillouin region obtained by the generalized Brillouin Hamiltonian quantity.
Many models of the Ermi case introduce many novel behaviors when the action of non-Ermi is introduced, such as the multibody behavior of non-Ermifermi superconductivity studied in the literature [48], where the non-Ermi term is the loss γ caused by the inelastic collision of twosomes. The barreden-Cooper-Schriefferv (BCS) effective Hamiltonian amount of non-Ermier paired swaths is
05
Quantum computing
Quantum computing has developed rapidly in recent years. The highly maneuverable and scalable nature of cold atoms makes it possible to achieve high-bit quantum entanglement, and the literature [52] is the first to propose that a quantum computer can be built with cold neutral atoms. Since 2010, Pan Jianwei's team at the University of Science and Technology of China has conducted research on ultracold atomic photolattices, realizing the entanglement of more than 600 pairs of ultracold 87Rb atoms with high fidelity[53] and simulating the arbitrary sub-excitation model of topological quantum computing.[54] In 2020, they first proposed a new atomic cooling scheme[55]: local chemical formulas were adjusted in the lattice so that insulated cold atomic samples alternated with a superfluid phase of large density (Figure 11(a)), where the atoms in the two phases were tunneled through exchange entropy, and the heat was stored in the superfluid phase in the form of low-energy excitation. By removing atoms from the super-fluid phase and regulating the lattice potential, a low-temperature uniform filling state of more than 104 points can be obtained. Through the hypercommunication of the three-energy level, 1250 pairs of two-atom bit entanglement gates can be obtained. From the measurements of spin correlation in Figure 11(b), it can be obtained that the fidelity of the experimentally generated density matrix is 99.3±0.1%, which is much higher than the fidelity of the neutral atomic two-qubit gate of the previous experiment.
06
epilogue
Cold atomic systems provide a completely new research platform due to their macroscopic quantum properties and highly controllable nature, and the study of novel quantum states and exotic physical properties is an internationally forward-looking and challenging frontier field. Cold atoms have important application value in the fields of quantum precision measurement, quantum simulation and quantum computing. As a multibody system that can be regulated at the microscopic scale, ultracold atoms have unique advantages in the study and regulation of macroscopic novel states of matter, and have become an important branch of physics. In the past decade, ultracooled atoms have presented many important new developments, providing a new perspective and reliable experimental platform for the realization and research of unconventional states of matter. Among them, the topological state study based on ultra-cold atoms extends from the topological insulation state without interaction or weak correlation to the interaction strong correlation system; the research on ultracold gas based on less internal degrees of freedom and short-range action is promoted to a new ultra-cold gas platform with multi-degree of freedom and long-range interaction, which effectively improves the simulation ability of the new multi-body physical state; the representation of the state of matter based on equilibrium state theory and the traditional research are advanced to the multi-body dynamic system away from equilibrium that is difficult to regulate in conventional condensed matter systems. It has spawned new concepts and basic theories for characterizing dynamic states of matter, and broadened the understanding of non-equilibrium physics. These unconventional multibody physical state studies are opening a new door to new physical fundamental laws and new scientific discoveries for condensed matter physics, statistical physics, non-equilibrium field theory and other physics disciplines, and will also enlighten new functional device technologies and high-tech industries.
Fruitful results have been achieved in the field of precision measurement based on the synthesis of cold atoms: cold atom fountain frequency scale, interferometer measurement gravitational constant, magic wavelength optical lattice frequency scale, cold ion frequency scale, cold atom gravity meter, cold atom gyroscope and other new cold atom precision measuring instruments are becoming measurement standards or many times refreshing the record of precision measurement, and some applications have also played an important role in exploration, military defense and so on. Extremely low thermal noise, good coherence, flexible maneuverability and extremely high signal-to-noise ratio make cold atom systems can be used to manufacture new quantum devices for quantum information, and also make them have great scientific significance and technical applications in the field of important quantum information such as quantum precision measurement, quantum information storage, and quantum information transmission. These research directions represent important strategic trends in the future development of information technology, are the focus of the next generation of quantum information systems that are fiercely competing in various countries in the world, and are very likely to have a huge impact on the economic development of human society.
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