Atoms ‘pumped’ into a quantum fluid from a Bose-Einstein condensate

Researchers have devised a method to construct a fractional quantum Hall fluid by “pumping” individual atoms into the exotic state using specifically shaped Raman beams. Alberto Tabarelli de Fatis of the Pitaevskii BEC Center, INO-CNR and Università di Trento, and colleagues detail a protocol to adiabatically prepare this many-particle fluid from a Bose-Einstein condensate, coherently adding atoms with well-defined angular momentum.

The work identifies an adiabatic path that avoids instabilities which typically limit the size of these systems, and numerically assesses the protocol’s efficiency for particle numbers exceeding current experimental capabilities. This approach demonstrates the benefit of using anharmonic confinement in realizing these complex quantum states.

Bose-Einstein Condensate Pumping Initiates Fractional Quantum Hall Fluid

This method bypasses traditional approaches that rely on finite-size systems and induced topological gaps, instead focusing on a coherent transfer of particles from a Bose-Einstein condensate. The resulting fluid exhibits properties stemming from the interplay of strong interactions and magnetic fields. This is achieved through an adiabatic path in the Fock space, a mathematical representation of the system’s quantum states, which prevents crossings of topological phase transitions.

An anharmonic confinement is important in realizing these complex quantum states, as the researchers specifically highlight its advantage in their work. This confinement, differing from harmonic potentials, allows for greater control over the interactions between atoms, stabilizing the fluid and enhancing its properties. The team’s approach uses a time-dependent coherent coupling, essentially a carefully orchestrated transfer of atoms between the condensate and the emerging fluid state.

By varying the strength and detuning of this coupling, the initial vacuum state is converted into the target Laughlin state, a specific configuration known to exhibit fractional quantum Hall behavior. The exact ground state minimizing angular momentum is the 1/2-Laughlin state, which resides within the lowest Landau level manifold, and is always nondegenerate with no interaction energy. The energy gap separating this ground state from excited states, denoted as E_g^(N), scales proportionally to the interaction strength and remains constant as the number of particles increases.

This constant gap is a key feature, ensuring the stability of the fluid against perturbations and allowing for longer observation times. The findings extend beyond atomic systems, with potential applications in photonic systems where tunable coherent pumps are readily available.

Synthetic magnetic fields combined with strong interactions are routinely realized in these platforms, and microwave photons can exhibit long lifetimes, making them ideal candidates for hosting fractional quantum Hall fluids. “Our proposal opens the way to the investigation of the exciting and elusive properties of fractional quantum Hall fluids in synthetic quantum matter,” the researchers state in their published work. Simulations performed by the team have demonstrated the protocol’s effectiveness with up to eight particles, and the results indicate the potential for scaling to systems containing a few tens of particles.

Adiabatic Preparation Avoids Topological Phase Transitions

This approach bypasses a critical limitation of earlier techniques by identifying an adiabatic pathway through the system’s quantum states that avoids topological phase transitions, instabilities that previously restricted the size and stability of these fluids. The team’s simulations demonstrate the protocol’s effectiveness in maintaining a sizable energy gap, important for preventing disruptions during the fluid’s formation. Unlike number-conserving schemes that rely on finite-size-induced topological gaps, this preparation method externally controls the protective energy gap via the amplitude of a coherent coupling.

This external control allows the system to maintain a significant gap throughout the adiabatic evolution, eliminating the need to alter the system’s Hamiltonian and, consequently, avoiding the problematic crossing of topological phase transitions. The use of Laguerre-Gauss Raman coupling, while explored previously, was limited by its reliance on spin flips, restricting the achievable angular momentum of the resulting fluid.

This new protocol circumvents that restriction by using a pump carrying angular momentum, directly inserting it into the system without rotating an external potential. The advantage of initiating the process with a Bose-Einstein condensate extends beyond simply providing atoms for the fluid; it removes the need for precise initial atom number control, a challenge that hampered earlier experiments.

Numerical assessments of the protocol reveal high fidelity values even for moderate-size systems, exceeding the capabilities of previous methods. For instance, a fidelity of 0.99 can be achieved for a system of four particles in 95 times the Rabi period (T_Ω), a six-fold improvement over theoretical proposals based on manipulating trapping frequency and ellipticity.

Raman Beams with Laguerre-Gauss Profiles Transfer Angular Momentum

Raman beams shaped with Laguerre-Gauss profiles deliver angular momentum to individual atoms, enabling the construction of a fractional quantum Hall fluid from an initially empty space. The technique, detailed in recent work, uses the beams to “pump” atoms into the fluid state from a surrounding Bose-Einstein condensate, effectively building the complex system particle by particle. Each atom receives a defined angular momentum while transitioning, driven by the unique properties of the Laguerre-Gauss beam profile.

This profile imparts an orbital angular momentum of l to each particle, contributing to the overall rotational characteristics of the forming fluid. The team’s approach uses a coupling mechanism, using the Raman beams to selectively transfer angular momentum, with the frequency difference of the beams encoding an effective detuning that controls the system’s evolution.

The simulations demonstrate the ability to prepare a Laughlin state, a specific type of fractional quantum Hall state, with a desired number of particles and total angular momentum. The researchers specifically designed the external pump with a single-particle angular momentum of l = N_t – 1, selecting the target particle number for the final state.

The inclusion of an anharmonic confinement potential is important for realizing these complex quantum states. The team’s Hamiltonian incorporates this potential, along with contact interactions between particles and the coupling strength determined by the Rabi coupling and the condensate’s order parameter. The researchers write. This ability to start from a vacuum state and build up the fluid through controlled atomic transfer represents a departure from methods requiring pre-existing systems. The simulations suggest a path toward samples containing tens of particles, significantly expanding the scope of experimental investigation into these exotic quantum states.

Anharmonic Confinement Enhances Adiabatic Gap Maintenance

An anharmonic confinement potential bolsters the stability of this method for creating fractional quantum Hall fluids, preventing the collapse of the delicate quantum state during preparation. Unlike previous approaches reliant on finite-size effects to maintain a gap in energy levels, this technique actively avoids topological phase transitions, sustaining coherence throughout the process. Numerical calculations reveal that the inclusion of this potential significantly reinforces adiabaticity, the gradual and stable evolution of the system, even when “pumping” atoms into the fluid.

This is particularly important as limitations in achieving perfect cylindrical symmetry in experimental setups can otherwise hinder rotation and destabilize the forming fluid. “The anharmonic and the plug potentials help keeping a sizable gap also in the middle of the ramp,” the researchers note, referring to the energy barrier important for maintaining the quantum state during atom transfer. The simulations, currently limited to eight particles due to computational constraints, demonstrate the potential for creating significantly larger samples than previously possible.

This is achieved through the broken degeneracy in specific sectors of the system, allowing for more robust control over the quantum state as more atoms are added. The resulting improvement in preparation times is promising for realizing fractional quantum Hall samples containing tens of particles, exceeding current experimental limitations. The robustness of this approach extends to addressing deconfinement issues, a common challenge in creating these exotic states of matter.

Rotating Frame Hamiltonian Models Synthetic Magnetic Fields

The inclusion of anharmonic confinement proves important for stabilizing the creation of a fractional quantum Hall (FQH) fluid. This approach relies on a synthetic magnetic field generated by rotating the reference frame, effectively mimicking the conditions necessary for FQH behavior without the need for physical magnetic fields. The team’s method begins with an empty two-dimensional trap and a Bose-Einstein condensate acting as a reservoir of atoms, coherently “pumped” into a strongly interacting state.

This transfer is facilitated by an external electromagnetic field, and the dynamics are described within a rotating frame where the Coriolis force generates the synthetic magnetic field. By carefully tuning the rotation frequency to match the trap frequency, the centrifugal potential largely cancels the harmonic confinement, leaving only residual anharmonic terms.

These anharmonic terms are essential for lifting the degeneracy of states and enhancing the stability of the FQH fluid. This is achieved by carefully controlling the transfer of atoms, ensuring a continuous and stable evolution towards the desired FQH state. The ability to avoid topological phase transitions is a key innovation, as it allows for the creation of larger and more robust quantum fluids. Beyond the stability benefits, the approach is also applicable to systems beyond ultracold atoms.

The underlying Hamiltonian describing the dynamics of the atoms is general enough to be adapted to photonic systems, where tunable coherent pumps and strong interactions are routinely realized. This opens the possibility of creating FQH fluids using photons, potentially leveraging their long lifetimes and unique properties for quantum information processing. The team’s findings represent a step toward realizing practical applications of FQH systems, offering a pathway to explore their complex behavior and harness their potential for advanced technologies.

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