Perspective on new implementations of atomtronic circuits

In this article, we provide perspectives for atomtronics circuits on quantum technology platforms beyond simple bosonic or fermionic cold atom matter-wave currents. Specifically, we consider (i) matter-wave schemes with multi-component quantum fluids; (ii) networks of Rydberg atoms that provide a radically new concept of atomtronics circuits in which the flow, rather than in terms of matter, occurs through excitations; (iii) hybrid matterwave circuits—a combination of ultracold atomtronic circuits with other quantum platforms that can lead to circuits beyond the standard solutions and provide new schemes for integrated matter-wave networks. We also sketch how driving these systems can open new pathways for atomtronics.

In this perspective article, we want to highlight a core aspect of the field: relying on the progress in cold atoms technology, the quantum fluid coursing through atomtronic networks can be of different nature ranging from weakly to strongly interacting particles, from short-to-long range, and with different statistical properties.The resulting systems enable blueprints for various devices and simulators with distinct specifications, performances, and functionalities.Specifically, we focus on atomtronic circuits of multicomponent gases, Rydberg atoms and hybrid devices, providing platforms beyond the standard bosonic or fermionic realizations.We will discuss how such circuits can provide new applications in quantum technology, for instance as interferometers, quantum simulators for high-energy physics and driven atomtronic circuits.

Multi-component gases
With the recent experimental developments, the field has progressed to a point where atomtronic networks of ultracold fermions can now be explored [61,62].Relying on the remarkable experimental achievements in the coherent control of N-component fermions/bosons [227][228][229][230], further progress can be envisaged.Indeed, the different internal states in the system add an extra level of complexity compared to a singlecomponent system [231][232][233][234][235][236] that can set atomtronic circuits with unique functionalities and specifications.An example is that of SU(N) fermions, as provided by alkaline earthlike gases [235,237,238], which are relevant both for quantum simulation [239][240][241][242][243] and for high-precision measurements [244,245].
A natural direction for multi-component atomtronics is that of quantum transport [10,11].Specifically, one could focus on fermionic transport, which, whilst extensively investigated in solid-state physics [246], could be revisited in new ways, owing to the specific features of the cold atoms technology [52].With a similar logic as that applied for two-component fermions [72,160,170,213,217,247], relevant problems like Josephson currents and the BEC-BCS crossover [248][249][250] can be studied for multicomponent systems.Persistent currents of multi-component systems in a ring track have been studied in [249,[251][252][253][254][255][256][257][258][259][260][261][262].Within multi-component ring-shaped lattices, it was shown that the angular momentum per particle in strongly correlated systems with SU(N) symmetry acquires fractional values of 1/N p (1/N) for repulsive [256] (attractive [249]) fermions and of 1/N p for repulsive bosons [262] where N p (N) is the number of particles (components).Such quantization properties are expected to result in an enhanced sensitivity to rotation as predicted for attractive one-component bosons [99,263].In this context, it would be worth exploring N-component matter-wave transport through localized weak links and impurity problems [264][265][266] on mesoscopic cold atoms rings [36,66,267].At the same time, the presence of one or more barriers in a ring circuit provides the basis for the realization of quantum electronic-inspired devices like Atomtronic Quantum Interference Devices (AQUIDs) [38,44,47,48,63,65,99,263,[268][269][270].Besides being interesting to study questions like macroscopic phase coherence, such systems can provide relevant platforms also for a matter-wave interferometry based on multi-component quantum fluids.
Digital Mirror Devices, painting techniques and Spatial Light Modulators have opened the way to study driven circuits [1][2][3].A single periodically driven Josephson junction in a strip of 6 Li atoms in BEC regime is predicted to display quantized dc-ac transitions [271].Such a phenomenon is the cold atoms counterpart of the Shapiro steps originally observed in the I-V characteristics of the superconducting Josephson junction [272,273].Shapiro steps in driven atomic Josephson junctions can be exploited to study emergent phenomena of superfluidity in the BEC-BCS crossover with a new twist.Analogously to their value in metrological voltage standards [274][275][276], driven Josephson junctions can define a useful tool to develop high-precision atomtronic circuitry, including more complex geometries, driven AQUIDs, or driven coupled arrays of atomic Josephson junctions.

Rydberg atoms
Rydberg atoms are atoms excited in states with a large principal quantum number.For this reason, they possess very distinctive properties including a large dipole moment that leads to a strong dipole-dipole interaction [277][278][279][280][281]. Atoms residing in the same Rydberg state effectively interact through a van der Waals-like potential with a characteristic 1/R 6 , with R being the atom-atom spatial distance [282,283].Instead, the dipole-dipole interactions of atoms in Rydberg states of opposite parity result in a spin exchange coupling that scales as 1/R 3 [284].The coherent local addressability and manipulation of Rydberg atoms in a large variety of spatial configurations have been thoroughly demonstrated [285][286][287][288].A spectacular phenomenon arising from the strong interaction is the dipole blockade for which only one atom in a characteristic spatial radius can be excited to a Rydberg state [289,290].Moreover, by shining on the systems with a suitable laser field, a specific detuning on the atomic energy levels can be induced, which ultimately results in a facilitation (or anti-blockade) mechanism [291][292][293].Controlling these blockade and anti-blockade protocols in networks of Rydberg atoms can provide a very versatile platform for quantum simulation [278,279,292].
Rydberg atoms can indeed define a new concept for atomtronics in that the flowing current in the circuits, rather than matter, can occur in terms of Rydberg excitations.Compared with the millisecond dynamics of cold atoms, Rydberg excitations can propagate on a microsecond time scales.As a result, faster atomtronic circuits and devices can be achieved.
Networks of Rydberg atoms are a promising platform to realize quantum state transfer, with multiple protocols being widely theoretically studied in quantum spin systems [294][295][296][297][298][299][300] and some being carried over with Rydberg atoms [301,302].The remarkable control on the parameters of the system, like the aforementioned local addressability obtained with optical tweezers [285,287,303] and interactions, gives the possibility to conceive atomtronic devices to transfer entangled and single excitation states.The basis to realize iconic quantum transport devices in mesoscopic physics like rf-and dc-SQUIDs has been proposed [304].An artificial gauge flux which results in a controllable flow of excitation in rings has been theoretically studied with different techniques [305,306] and experimentally realized for small systems [307].Putting together these two features and considering the flexibility of the geometry, Rydberg atoms can constitute a promising platform for the realization of interference devices based on excitation currents, they can also be used to propose and implement sourcedrain quantum transport with new and exotic channel configurations.
By suitable engineering of the dipole anti-blockade, Rydberg atomtronic circuits emulating electronic devices, such as a diode, switches and logical gates have been proposed [308].With this set of devices, the development of more intricate gadgets and more complex circuits can be proposed, examples may include adders and routers, which can be conceived through the implementation of the universal logical gate set.In addition, the manipulation of dissipation [309] also defines a further knob to manipulate the Rydberg atomtronic circuits dynamically, which can be used for conceiving new devices as well as devising quantum simulation of driven-dissipative systems [292,310,311].
Another promising pathway of research, that exploits the potential and control offered by Rydberg atom platforms, is the quantum simulation of high-energy physics.This field has recently attracted the interest of a very heterogeneous community, aimed at exploiting quantum technologies to study physical phenomena, such as confinement, which are elusive by nature.In this context, digital and quantum simulations of lattice gauge theories (LGTs) have been widely explored in several platforms, ranging from ultracold atoms in optical lattices [312][313][314][315][316][317][318][319] and Rydberg atoms [320][321][322], to trapped ions [323][324][325] and superconducting circuits [326][327][328][329]. Rydberg atoms, which interact according to a Van der Waals-like behaviour, naturally implement the gauge-invariant dynamics of fermionic matter coupled to Z 2 gauge fields in a specific gauge sector [330].These allow for the study of coherence properties of confined matter, such as the peculiar Aharonov-Bohm oscillations that emerge, at the mesoscopic scale, in the presence of an external magnetic flux [331].Such magnetic flux could be experimentally implemented through Floquet driving schemes applied to the detuning of the atoms, thus realizing a coherent current of confined matter.In these cases, the control over the experimental parameters in a Rydberg atom platform is instrumental.Indeed, the time scales required for the observation of the effective gauge invariant real-time dynamics are within reach of the currently attained experimental times.

Hybrid devices
As quantum technologies continue to advance, the seamless integration of atomtronic circuits with established technologies becomes increasingly important.This requires capitalizing on the unique features of different quantum systems to construct hybrid quantum circuits with enhanced capabilities compared with classical counterparts, thus enabling to unlock new technologies.Examples of hybrid systems based on ultracold atoms include the use of cavities [332,333] as well as superconducting circuits disks [334], films [335], wires [336] and rings [337].
Many hybrid systems stem from the extensive overlap between distinctive fields.A prime example is the fusion of quantum optics and ultracold matter.These two domains have been mutually beneficial ever since the inception of ultracold matter.An example of such a hybridization can be found in the use of optical nanofibers surrounded by a cloud of cold atoms, where the interaction between light and matter is facilitated by the evanescent field generated by the nanofiber [338][339][340][341] which can also be used to create spatially dependent artificial magnetic fields with new and exciting phenomena [342][343][344][345][346]. Extending hybrid circuits of ultracold atoms coupled with superconductors can be very relevant for quantum technologies.The general idea behind is that in a schematic information processing protocol, gate operations and state preparations can be carried out in the fast solid-state apparatus; then transferred and stored in atomic systems that are less prone to decoherence and finally transferred back to solid-state devices for further processing.Relying on the sensitivity of the atomic spins to microwaves [347,348], coupled systems of atoms and superconducting elements have been proposed [349][350][351][352][353][354][355][356].The fabrication of various magnetic traps for ultracold atoms on superconducting atom chips [335,337,[357][358][359][360][361] together with the studies in quantum information processing on coupling ultracold atoms and superconducting chips [362][363][364][365][366] paves the way towards the realization of an atomic quantum memory linked to superconducting quantum circuits.
More recently, the combination of the large coherence times of ultracold matter with opto-mechanics has been proposed as a hybrid system that can provide much higher sensitivity and control of the atoms.In particular, this technology can allow us to probe weakly interacting bosonic atoms in a non-destructive way [332] as well as probing more sensitive regimes such as attractively interacting bosonic systems that can form solitonic states with application to interferometry [333].Remarkably, due to the long coherence times provided by the cold atoms, their use in the context of quantum memories has been considered for integrated quantum computation.In particular, these systems provide advantages in both coherence times and high retrieval rates by making use of the aforementioned control on the light-matter interaction [367,368].Expanding these hybridizations between atomtronics and quantum technologies is especially important in the fields of sensing and simulation.By utilizing the unique characteristics of different platforms, such as the ones discussed in this perspective, we can significantly broaden the scope of the field, unlocking the full potential of quantum systems and promoting progress in this rapidly evolving field.

Conclusions
In this article, we highlight how new platforms in cold atoms quantum matter, other than the simple bosonic or fermionic degenerate gases, can open up new research opportunities in atomtronics-enabled quantum technologies.We focused on three specific platforms defining research directions with great potential: multi-component gases, Rydberg atoms and hybrid systems.Key areas that can benefit from these are matter-wave sensing technology and quantum simulations with reduced time scales.
To close this article we comment on the important role that machine learning can have on the design and control of the future atomtronic quantum technologies.Indeed, through machine learning optimization has been already implemented in specific experimental schemes of ultracold bosonic systems as cooling processes [369,370] readout protocols [371][372][373].The new implementations discussed in this perspective can also profit from these techniques.In particular, Reinforcement Learning (RL) where one can analyze complex systems without the need of prior knowledge, can provide a practical solution for the system's experimental control problems without relying on assumptions about system and manual analysis.Recent examples in experimental atomtronics circuits include the use of RL for optimizing matter-wave interferometer [374,375] and for imparting persistent currents in ring geometries [69,376].Nonetheless, the possibilities offered by machine learning in atomtronics circuits are ample, and a vast territory is unexplored.Further developing proof of concept devices that use machine learning as a tool to drive quantum matter, being either multi-component gases or Rydberg, would broaden the field; on the other way around, atomtronicsinspired machine learning schemes can find applications in other quantum technologies [374,375].Finally, quantum technologies on the cloud, such as Infleqtion (ColdQuanta) for cold atoms [377] or QuEra for Rydberg atoms [378], can open new important avenues for the field.