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(a) Level diagram (i) and schematic (ii) for a two-photon Raman transition between jg 1 ; p 0 i and jg 2 ; p 0 þ 2 hki. Atoms with initial momentum p 0 are illuminated with light from two counter-propagating lasers of frequencies x 1 and x 2 and wavevectors k and Àk, respectively. D is the one-photon detuning from some excited state jei and d is the two-photon detuning, which depends upon the momentum of the atoms. When D ) d and x 1 À x 2 % x 0 , atomic population in jg 1 i can be resonantly transferred to jg 2 i, accompanied by a 2 hk momentum kick to the atoms, as shown in (a-ii). (b) Level diagram (i) and schematic (ii) for a 2n-photon Bragg transition between jg; p 0 i and jg; p 0 þ 2n hki. The solid parabolic curves are the free atom dispersion relations between momentum p and energy E for the ground and excited internal states. Here d B ¼ 4x r , where x r ¼ hk 2 =ð2mÞ is the recoil frequency (k ¼ jkj), and the two-photon detunings are d m ¼ 4mðn À mÞx r . Provided the one-photon detunings D m are much larger than d m and x 1 À x 2 % nd B , a 2n-photon transition couples momentum eigenstates jpi and jp þ 2n hki via 2n À 1 intermediate states (horizontal dashed lines). These intermediate states are negligibly populated provided the effective 2n-photon Rabi frequency is small compared to d m.
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Quantum entanglement has been generated and verified in cold-atom experiments and used to make atom-interferometric measurements below the shot-noise limit. However, current state-of-the-art cold-atom devices exploit separable (i.e., unentangled) atomic states. This perspective piece asks the question: can entanglement usefully improve cold-atom se...
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... rotation measurement requires a space-time separation of the matter-waves that form the two interferometer arms. 94 Current state-of-the-art cold-atom accelerometers and gyroscopes effect beam splitting with standing waves of light, formed via two counter-propagating laser pulses tuned to drive Raman 95 or Bragg 96 transitions in the atoms (see Fig. 2). In the standard Mach-Zehnder configuration where the atoms are in free fall, a uniform acceleration a induces a relative phase shift between the two interferometer arms: 95 / ¼ k Á aT 2 , where hk is the momentum imparted by the beamsplitters and mirrors and T is the time between pulses (interrogation time). This phase can be ...
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... Conclusion.-Momentum entanglement of ultracold atoms holds great potential for enhancing matter wave interferometry [107]. We have theoretically and numerically explored two methods for producing momentum multiparticle entangled (Dicke-squeezed) states of atoms with one internal ground state (spin-0) by nonlinear selforganization in driven systems. ...
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... Atom interferometry is capable of providing state-ofthe-art measurements of gravitational fields [1][2][3][4][5][6][7], gravitational gradients [8][9][10][11][12][13], and magnetic fields [14], with future applications such as minerals exploration [15,16], hydrology [17], inertial navigation [18][19][20], and possible tests of candidate theories of quantum gravity [21][22][23]. There is considerable recent interest in the use of quantum entanglement in atom interferometry [24][25][26], which would improve the precision, measurement rate, and reduce the overall size of these devices [25]. Two of the most promising routes to generating useful entanglement are spin-squeezing via One-Axis Twisting (OAT) [27][28][29][30], or via Quantum non-deomolition (QND) measurements [31][32][33][34][35][36][37]. ...
... Atom interferometry is capable of providing state-ofthe-art measurements of gravitational fields [1][2][3][4][5][6][7], gravitational gradients [8][9][10][11][12][13], and magnetic fields [14], with future applications such as minerals exploration [15,16], hydrology [17], inertial navigation [18][19][20], and possible tests of candidate theories of quantum gravity [21][22][23]. There is considerable recent interest in the use of quantum entanglement in atom interferometry [24][25][26], which would improve the precision, measurement rate, and reduce the overall size of these devices [25]. Two of the most promising routes to generating useful entanglement are spin-squeezing via One-Axis Twisting (OAT) [27][28][29][30], or via Quantum non-deomolition (QND) measurements [31][32][33][34][35][36][37]. ...
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... Generalizing to the quantum case, the concept of the number of resources is greatly extended. It has been demonstrated that if quantum resources, such as entanglement [4][5][6][7] or squeezing [8][9][10], are used, the metrological sensitivity can surpass the classical SNL [2,3,8,[11][12][13][14]. Thus, the numbers of the entangled particles, the squeezing parameter, and the sizes of the many-body systems experiencing a quantum phase transition, are generally regarded as the number of quantum resources. ...
Quantum metrology pursues the physical realization of higher-precision measurements to physical quantities than the classically achievable limit by exploiting quantum features, such as quantum entanglement and squeezing, as resources. It has potential applications in developing next-generation frequency standards, magnetometers, radar, and navigation. However, the ubiquitous decoherence in the quantum world degrades the quantum resources and forces the precision back to or even worse than the classical limit, which is called the no-go theorem of noisy quantum metrology and greatly hinders its applications. Therefore, how to realize the promised performance of quantum metrology in realistic noisy situations attracts much attention in recent years. We will review the principle, categories, and applications of quantum metrology. Special attention will be paid to different quantum resources that can bring quantum superiority in enhancing the sensitivity. Then, we will introduce the no-go theorem of noisy quantum metrology and its active control under different kinds of noise-induced decoherence situations.
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... This bound is given by ∆ 2 (θ A − θ B ) SQL = 4/N , where N is the total number of particles [37,41]. A promising research goal is to devise feasible schemes that reduce the quantum noise in interferometric measurements and, in particular, overcome the SQL with the use of quantum resources [42,43]. ...
Thanks to common-mode noise rejection, differential configurations are crucial for realistic applications of phase and frequency estimation with atom interferometers. Currently, differential protocols with uncorrelated particles and mode-separable settings reach a sensitivity bounded by the standard quantum limit (SQL). Here we show that differential interferometry can be understood as a distributed multiparameter estimation problem and can benefit from both mode and particle entanglement. Our protocol uses a single spin-squeezed state that is mode-swapped among common interferometric modes. The mode swapping is optimized to estimate the differential phase shift with sub-SQL sensitivity. Numerical calculations are supported by analytical approximations that guide the optimization of the protocol. The scheme is also tested with simulation of noise in atomic clocks and interferometers.
... Similar approaches have been explored with ultracold atomic gases to correlate massive particles either in their internal [6][7][8][9][10][11][12] or motional [13][14][15][16][17][18][19][20][21][22][23][24][25] degrees of freedom. Quantum metrology based on atom interferometry, including precision gravitometry and magnetometry [26,27], would benefit from a rapid pair production in well-defined momentum modes. However, existing schemes relying on collisions are limited by the timescales of contact interactions. ...
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... This bound is given by ∆ 2 (θ A − θ B ) SQL = 4/N, where N is the total number of particles [36,40]. A promising research goal is to devise feasi-ble schemes that reduce the quantum noise in interferometric measurements and, in particular, overcome the SQL with the use of quantum resources [41,42]. ...
Thanks to common-mode noise rejection, differential configurations are crucial for realistic applications of phase and frequency estimation with atom interferometers. Differential interferometry can be understood as a distributed multiparameter estimation problem and can benefit from both mode and particle entanglement. Currently, differential protocols with uncorrelated particles and mode-separable settings reach a sensitivity bounded by the standard quantum limit (SQL). Here, we propose to overcome the SQL by exploiting spin-squeezing in an atomic quantum network. A single spin-squeezed state is mode-swapped among common interferometric modes. The mode swapping is optimized to estimate the differential phase shift with sub-SQL sensitivity. Numerical calculations are supported by analytical approximations that guide the optimization of the protocol. The scheme is also tested with simulation of noise in atomic clocks and interferometers.
... Quantum metrology, which promises higher measurement precision for parameter estimation by exploiting quantum resources such as entanglement and quantum correlations [1], can allow sensing precision that surpasses the fundamental shot-noise limit of sensors with classical states [2][3][4]. Entanglement have been used to surpass the shot-noise limit in atomic clocks [5][6][7][8][9][10], magnetometers [5,[11][12][13][14][15][16], and numerous proposals and proof-of-principle demonstrations suggest that entanglement-enhanced atomic inertial sensors will be realized in the near future [7,14,[17][18][19][20][21][22]. For N uncorrelated particles, such as spin coherence state (SCS), the measurement precision can only reach the standard quantum limit (SQL) [23], which scales as ∝ 1/ √ N. By employing entanglement among particles, entangled multiparticle states such as spin squeezed state [24,25], Greenberger-Horne-Zeilinger state [26,27], twin-Fock states [28][29][30] can beat the SQL or even approach the Heisenberg limit (HL) [31][32][33], i.e., ∝ 1/N. ...
Entanglement is one of the key ingredients for enhancing the measurement precision of quantum sensors. Generally, there is a trade-off between state preparation and sensing within a limited coherence time. To fully exploit temporal resources, concurrent entanglement generation and sensing with designed sequence of rotations are proposed. Based on twist-and-turn dynamics, modulated rotations along only one axis may be sufficient to drive the state to the optimal one for tiny estimated parameter. However, when the estimated parameter is not tiny, it may impact the evolved state and hence degrade the final measurement precision. Here, we introduce another modulated rotations along different axis and find out the optimal control sequences by means of machine optimization. The optimal measurement precision bounds become independent on the estimated parameter, which improves the dynamic range of the machine designed sensors. Particularly, by optimizing the interaction strength for different particle number and the time-modulated rotations along two different axes via machine optimization, the Heisenberg-limited precision scaling can be attained. Our work points out a way for designing optimized quantum-enhanced metrology protocols, which is promising for developing practical quantum sensors.
... Cold atom experiments have over the last two decades emerged as a very strong contender for the study of fundamental physics and for the simulation of quantum behavior relevant for other branches of physics (Bloch et al., 2008;Zohar et al., 2015;Saffman, 2016;Gross and Bloch, 2017;Szigeti et al., 2021). One particular intriguing problem that has been addressed is the quantum many-body problem, which has excited researchers and students over decades. ...
Cold atomic gases have become a paradigmatic system for exploring fundamental physics, while at the same time allowing to explore applications in quantum technologies. The accelerating developments in the field have led to a highly advanced set of engineering techniques that, among others, can tune interactions, shape the external geometry, select among a large set of atomic species with different properties, as well as control the number of atoms. In particular, it is possible to operate in lower dimensions and drive atomic systems in the strongly correlated regime. In this review, we discuss recent advances in few-body cold atom systems confined in low dimensions from a theoretical viewpoint. We mainly focus on bosonic systems in one dimension and provide an introduction to the well-known static properties before we discuss the state-of-the-art quantum dynamical processes stimulated by the presence of correlations. Besides describing the fundamental physical phenomena arising in these systems, we also provide an overview of the tools and methods that are commonly used, thus delivering a balanced and comprehensive overview of the field. We conclude by giving an outlook on possible future directions that are interesting to explore in these correlated systems.
