# ATOMTRONICS PDF DOWNLOAD

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PDF | Abstract at away in Earth orbit. Atomtronics seeks to shift even more work to atomic media, using ultracold Download full-text PDF. Atomtronics is an emerging sub-field of ultracold atomic physics which encompasses a broad . Create a book · Download as PDF · Printable version. Status – Atomtronics is an emerging field seeking to realize atomic circuits exploiting ultra-cold atoms manipulated in micro-magnetic or laser-generated.

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Atomtronic setups are characterized by enhanced flexibility and control of the fundamental mechanisms underlying their functionalities and by. This content was downloaded from IP address on 22/06/ at Focus on atomtronics-enabled quantum technologies. Atomtronics is an emerging field in quantum technology that promises to realize ' atomic circuit' architectures exploiting ultra-cold atoms manipulated in versatile.

This work contrasts the above mentioned studies in that it applies to a system with very low number of degrees of freedom. A simple means of breaking integrability in the model is through an applied external field. Generally, it might be expected that this will drive the system into a chaotic dynamical regime.

However it is shown that in certain circumstances the changing dynamics of the model, through tuning of the external field, can be predicted with remarkable accuracy. The result can be understood by revealing the structure of a hidden subsystem within the model. This level of control points towards the potential utility of a physical realization of the model as a quantum switch. Later, it will be shown that Q assumes a fundamental role in the analysis of resonant 30 quantum dynamics of the system 2.

This arises due to an unexpected connection with virtual processes. Details are provided in Methods.

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Further details about the integrability, and associated exact solvability, have been established. This was achieved through the Yang-Baxter equation and Bethe Ansatz methods This is schematically shown in Fig. It is important to observe that the above Hamiltonian still commutes with the operator N.

## atomtronics

Adopting the same classification for the integrable three-well system given by 2 , numerical computation of the energy spectrum shows that transition from the Rabi to the Josephson regime is accompanied by the emergence of energy bands. Illustrative results are depicted in Fig. Note that the separation into distinct energy bands becomes very evident once the system is deep into the Josephson regime.

In the Rabi regime, an accurate description of the initial state requires a linear combination over all eigenstates.

This conclusion applies for all particles numbers, with the result represented in Fig. Moreover, it will be shown how the breaking of the integrability, through the application of an external field, allows for control of the dynamics in a predictable fashion.

Results are shown for 2 in dimensionless units. The region marked with a circle on a and c is enlarged in b and d.

We begin with the integrable model 2 and first consider variations in the interaction parameter U to manipulate the tunneling across the wells.

## From electronics to atomtronics

The dynamics typically display collapse and revival of oscillations in the Rabi regime, as in Fig. The transition between the Rabi and Josephson regimes can be seen, qualitatively, in the passage from Fig. This change in behavior is in accord with the threshold point in Fig.

Dimensionless units are used. It is apparent that increasing U leads to an increasing suppression of tunneling into the gate, while maintaining oscillations between the source and the drain. In the case d, the expectation value of the number operator associated with the gate is negligible, so tunneling to the gate is considered to be switched-off. The oscillations between the source and the drain are close to being harmonic and coherent Full size image In this latter regime, Fig.

As is known 1 , 2 , 31 , the self-trapping regime is expected to occur in the two-well model in the Josephson regime. In Fig. For d the expectation value of the number operator associated with the drain is negligible, so tunneling into the drain is considered to be switched-off Full size image Control of resonant tunneling In Fig. This behavior supports the conclusion that the effective Hamiltonian for the resonant tunneling regime is simply related to the conserved charge Q.

The three points highlighted in the curves correspond to the values of the amplitude and frequency of Fig. The markers in the curves correspond to the values of the amplitude of Fig.

In agreement with Chuang et al. Discussion We have analyzed a model for boson tunneling in a triple-well system. This was conducted in both integrable and non-integrable settings through variation of coupling parameters. The model draws an analogy with a transistor through identification of the wells as the source, gate, and drain. Our primary objective was to investigate how this model could be implemented as an atomtronic switching device. In the integrable setting, we identified the resonant tunneling regime between the source and drain, for which expectation values of particle numbers in the gate are negligible.

Moreover, it was found that a conserved operator of the integrable system acts as an effective Hamiltonian, which predicts coherent oscillations. This is in agreement with observations from numerical calculations. We then broke integrability through application of an external field to the source and the drain.

It was shown in Fig. On the other hand, in the resonant tunneling regime, the field did not destroy the harmonic nature of the oscillations, but did influence the amplitude and frequency.

Increasing the applied field allowed for tuning the system from the switched-on configuration through to switched-off Fig. Results from semiclassical analyses produced formulae for the amplitude and frequency, which proved to be remarkably accurate when compared to numerical calculations. This demonstrates the possibility to reliably control the harmonic dynamical behavior of the model in a particular regime.

A surprising feature of this result is that the ability to control the system in a predictable manner arises through the breaking of integrability. Our results open possibilities for multi-level logic applications and consequently new avenues in the design of atomtronic devices.

It is important, finally, to comment on the limitations of a three-mode Hamiltonian in the description of cold atom systems in a triple-well potential.

Contributions from higher energy levels of the single-particle spectrum cannot be ignored under certain coupling regimes. For example, the presence of the external field will ultimately lead to level crossings as the field strength is increased. In the case of the analogous double-well system, estimates for when this may occur have been formulated A three-well system opens up wider possibilities for physical behaviors 5 , 6 , 7 , most notably as an ultracold version of a transistor 8 , or similar type of switching device.

The individual wells can be identified as the source, gate, and drain, potentially forming a building block in the emerging field of atomtronics 9 , 10 , This prospect is driving research into transistor-like structures beyond the electronic domain 12 , Here we investigate the influence of integrability in the control of tunneling in a triple-well system.

To do so, we must go beyond the familiar three-well Bose—Hubbard model 14 , 15 , 16 , 17 , 18 , and consider a more general system which facilitates an integrable limit. Such a model has already been introduced into the literature. It models dipole—dipole interactions and the tunneling between adjacent sites for a population of ultracold dipolar bosons with large dipole moment, such as chromium or dysprosium, loaded in an aligned triple-well potential.

Both of these can be either attractive or repulsive, which in principle allows for the manufacture of weak net on-site interaction. Although the DDI follows an inverse cubic law, it is also dependent on the angle between dipole orientation and the displacement between dipoles.

In combination with the geometry of the trap potential viz. Importantly, this includes the possibility for the inter-well couplings Uij to have greater magnitude than the on-site coupling U0. The experimental feasibility of this system for dipolar bosons was detailed by Lahaye et al. The wells are aligned along the y-axis, separated by a distance l, with bosons polarized by a sufficiently large external field along the z-direction.

See Methods for further details. In this limit there exists an additional conserved operator besides the Hamiltonian and the total particle number, such that the number of independent conserved operators is equal to the number of degrees of freedom.

While for classical systems integrability is well-known to prohibit chaotic behavior, the consequences for quantum system are less understood 21 , Notwithstanding, it is recognized that quantum integrability has far reaching impacts. One route to characterize the degree of chaoticity in a quantum system is through energy level spacing distributions Integrable systems tend to display Poissonian distributions 24 , while non-integrable systems generally observe the Wigner surmise 25 following the Gaussian Orthogonal Ensemble, or similar 26 , Here we demonstrate how integrability, and the breaking of it, can be utilized to investigate tunneling dynamics.

This work contrasts the above mentioned studies in that it applies to a system with very low number of degrees of freedom.

A simple means of breaking integrability in the model is through an applied external field. Generally, it might be expected that this will drive the system into a chaotic dynamical regime. However it is shown that in certain circumstances the changing dynamics of the model, through tuning of the external field, can be predicted with remarkable accuracy.

The result can be understood by revealing the structure of a hidden subsystem within the model. This level of control points towards the potential utility of a physical realization of the model as a quantum switch. Later, it will be shown that Q assumes a fundamental role in the analysis of resonant 30 quantum dynamics of the system 2.

This arises due to an unexpected connection with virtual processes. Details are provided in Methods.

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Further details about the integrability, and associated exact solvability, have been established. This was achieved through the Yang-Baxter equation and Bethe Ansatz methods This is schematically shown in Fig.

It is important to observe that the above Hamiltonian still commutes with the operator N.

Adopting the same classification for the integrable three-well system given by 2 , numerical computation of the energy spectrum shows that transition from the Rabi to the Josephson regime is accompanied by the emergence of energy bands. Illustrative results are depicted in Fig.

Note that the separation into distinct energy bands becomes very evident once the system is deep into the Josephson regime. In the Rabi regime, an accurate description of the initial state requires a linear combination over all eigenstates. This conclusion applies for all particles numbers, with the result represented in Fig. Moreover, it will be shown how the breaking of the integrability, through the application of an external field, allows for control of the dynamics in a predictable fashion.

Results are shown for 2 in dimensionless units. The region marked with a circle on a and c is enlarged in b and d. We begin with the integrable model 2 and first consider variations in the interaction parameter U to manipulate the tunneling across the wells.

The dynamics typically display collapse and revival of oscillations in the Rabi regime, as in Fig. The transition between the Rabi and Josephson regimes can be seen, qualitatively, in the passage from Fig.

This change in behavior is in accord with the threshold point in Fig. Dimensionless units are used. It is apparent that increasing U leads to an increasing suppression of tunneling into the gate, while maintaining oscillations between the source and the drain. In the case d, the expectation value of the number operator associated with the gate is negligible, so tunneling to the gate is considered to be switched-off.

The oscillations between the source and the drain are close to being harmonic and coherent Full size image In this latter regime, Fig. As is known 1 , 2 , 31 , the self-trapping regime is expected to occur in the two-well model in the Josephson regime. In Fig. For d the expectation value of the number operator associated with the drain is negligible, so tunneling into the drain is considered to be switched-off Full size image Control of resonant tunneling In Fig.

This behavior supports the conclusion that the effective Hamiltonian for the resonant tunneling regime is simply related to the conserved charge Q.

## Quantum Physics

The three points highlighted in the curves correspond to the values of the amplitude and frequency of Fig. The markers in the curves correspond to the values of the amplitude of Fig.Three parallel lasers blue are crossed by a transverse beam green. A surprising feature of this result is that the ability to control the system in a predictable manner arises through the breaking of integrability.

It models dipole—dipole interactions and the tunneling between adjacent sites for a population of ultracold dipolar bosons with large dipole moment, such as chromium or dysprosium, loaded in an aligned triple-well potential. We consider a system of bosons with dipole—dipole interactions to provide long-range interactions, and weakly repulsive contact interactions to promote condensate stability This is then used for design of cooling and trapping apparatus that is later realised experimentally and described.

Finally, Atomtronics may also provide new solutions for the physical realization of quantum gates for quantum information protocols and hybrid quantum systems. The result can be understood by revealing the structure of a hidden subsystem within the model. Such a model has already been introduced into the literature.

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