Spin-orbit Coupling Enables Precise Control of Bose-Einstein Condensates for Physics Applications

Controlling Bose-Einstein condensates promises advancements in fields ranging from quantum information processing to condensed matter physics. Yue Ban of Shanghai University, alongside Xi Chen, J.G. Muga and E. Ya Sherman, detail new protocols for simultaneously manipulating both the internal and motional states of these ultracold atoms when subjected to spin-orbit coupling within a Morse potential. Their research demonstrates how state transitions can be achieved through carefully designed Raman coupling and detuning, offering a pathway to precise quantum state engineering. Significantly, the team’s approach proves robust against common experimental imperfections and scales effectively, even when accounting for interatomic interactions, paving the way for more complex and reliable quantum systems.

Raman Control of Spin-Orbit Coupled BECs

Scientists engineered a novel approach to exert complete control over a Bose-Einstein condensate, a state of matter with potential applications in quantum information processing and condensed matter physics. The research focused on simultaneously manipulating both the internal ‘pseudospin’ and motional states of a spin-orbit-coupled condensate trapped within a specifically shaped Morse potential. This intricate control was achieved through the application of Raman coupling and carefully designed, time-dependent detuning terms, a technique based on invariant-based inverse engineering. The study pioneers a method for state transition within the condensate by precisely tailoring these parameters, offering a pathway to manipulate quantum systems with unprecedented accuracy.

The experimental setup involved trapping ultracold bosonic atoms within a one-dimensional Morse potential, created using two evanescent light waves. Characterized by parameters representing energy and inverse length, this potential transitions from harmonic confinement to a constant potential, effectively creating a free particle as the inverse length approaches zero. Researchers established a dimensionless system, scaling units of length, energy, time, and velocity based on the parameters of the Morse potential, simplifying the effective Schrödinger equation. Normalized orbital states were then calculated using Laguerre polynomials and Euler gamma functions, forming the basis for manipulating the condensate’s quantum state.

To drive transitions between internal states, the team harnessed a Raman laser configuration coupling two pseudospin states. The system is described by a Hamiltonian incorporating momentum, the Morse potential, a time-dependent Raman coupling strength, a detuning term, and a spin-orbit coupling strength due to the Doppler effect. By carefully designing the time evolution of the Raman coupling and detuning using a two-level algorithm derived from inverse engineering, the researchers demonstrated high-fidelity transfer of the condensate’s state. This method achieves precise control by establishing an effective two-level system, operating under conditions where energy gaps between states are significantly different and operating times are much greater than a reciprocal energy difference.

A key innovation of the work lies in the construction of a dynamical invariant, which governs the system’s evolution. This invariant, expressed in terms of polar and azimuthal angles, allows for the identification of orthogonal eigenstates and the derivation of solutions to the time-dependent Schrödinger equation. The approach enables the creation of superposition states, crucial for quantum information processing, and demonstrates robustness against laser-field noise and systematic device-dependent errors. By generalizing the inverse engineering method to interacting Bose-Einstein condensates through an ansatz on the Bloch sphere, the study expands the applicability of this technique to more complex quantum systems.

Complete Control of Condensate Spin and Motion

Scientists achieved complete control over a Bose-Einstein condensate, demonstrating a pathway towards advancements in information processing and condensed matter physics. The research details protocols for simultaneously manipulating both the internal pseudospin-1/2 states and the motional, position-related states of a spin-orbit-coupled Bose-Einstein condensate confined within a Morse potential. Experiments revealed that state transitions can be implemented through precisely designed Raman coupling and detuning terms, utilising a technique known as invariant-based inverse engineering. This control extends to driving state transfer by tuning the direction of the spin-orbit-coupling field and modulating the magnitude of the effective synthetic magnetic field.

Results demonstrate the ability to generalise this approach to interacting condensates by dynamically adjusting the time-dependent detuning to account for interatomic interactions, paving the way for complex quantum simulations. Measurements confirm the robustness of the proposed protocols against laser-field noise and systematic device-dependent errors, crucial for practical implementation. Further investigation focused on the dynamics of the spin-orbit-coupled Bose-Einstein condensate within the Morse potential, employing inverse engineering to tailor the control parameters. The study leverages the unique properties of the Morse potential, where level spacing decreases as energy approaches the continuous spectrum and spatial asymmetry enables simultaneous internal state control and position displacement.

Scientists designed time-dependent Raman coupling and detuning to control both internal and motional states in a non-interacting condensate, demonstrating the algorithm’s applicability to more complex, multi-level systems. Tests prove that the amplitude of the external synthetic magnetic field and the direction of the spin-orbit-coupling field can be selected as tunable parameters to simultaneously control the internal state and the position transfer. The breakthrough delivers a method for achieving state transfer by manipulating the direction of the spin-orbit-coupling field and modulating the level detuning, extending the inverse engineering method to interacting Bose-Einstein condensates through a Bloch sphere-based ansatz for state evolution. Data shows the potential for interferometric applications, where each interferometer arm experiences distinct effects due to the combined control of internal states and position.

Condensate Control via Raman Coupling and Algorithms

Researchers have demonstrated protocols for the simultaneous control of both internal and motional states within a spin-orbit-coupled Bose-Einstein condensate, a system with potential applications in areas like quantum information processing and condensed matter physics. By employing Raman coupling and carefully designed detuning terms, alongside manipulation of the spin-orbit coupling field, they achieved controlled state transitions within the condensate. This control extends to interacting condensates through adjustments to the time-dependent detuning, effectively compensating for interatomic interactions.

The work introduces a robust two-level algorithm for inverse engineering, proving its accuracy even when applied to more complex, multilevel systems. This algorithm successfully manages state transfer by manipulating the direction of the spin-orbit coupling field and the level detuning, all within the framework of a Morse potential. While the authors acknowledge that the presented models rely on specific assumptions regarding the experimental setup, they demonstrate the protocol’s resilience to common experimental imperfections like laser-field noise and systematic errors. Future research could explore the practical implementation of these control protocols in physical systems and investigate their scalability to larger, more complex condensates. The authors suggest that extending the current framework to explore more intricate quantum algorithms and potentially harnessing the condensate for specific quantum tasks represents a logical next step. These findings contribute to the growing field of ultracold atom manipulation, offering a pathway towards greater precision and control in quantum systems.