Entangled states of rotating, trapped ultracold bosons form a very promising scenario for quantum metrology. In order to employ such states for metrology, it is vital to understand their detailed form and the enhanced accuracy with which they could measure phase, in this case generated through rotation. In this work, we study the rotation of ultracold bosons in an asymmetric trapping potential beyond the lowest Landau level (LLL) approximation. We demonstrate that while the LLL can identify reasonably the critical frequency for a quantum phase transition and entangled state generation, it is vital to go beyond the LLL to identify the details of the state and quantify the quantum Fisher information (which bounds the accuracy of the phase measurement). We thus identify a new parameter regime for useful entangled state generation, amenable to experimental investigation.
Entangled states of rotating, trapped ultracold bosons form a very promising scenario for quantum metrology. In order to employ such states for metrology, it is vital to understand their detailed form and the enhanced accuracy with which they could measure phase, in this case generated through rotation. In this work, we study the rotation of ultracold bosons in an asymmetric trapping potential beyond the lowest Landau level (LLL) approximation. We demonstrate that while the LLL can identify reasonably the critical frequency for a quantum phase transition and entangled state generation, it is vital to go beyond the LLL to identify the details of the state and quantify the quantum Fisher information (which bounds the accuracy of the phase measurement). We thus identify a new parameter regime for useful entangled state generation, amenable to experimental investigation.
Entangled states of rotating, trapped ultracold bosons form a very promising scenario for quantum metrology. In order to employ such states for metrology, it is vital to understand their detailed form and the enhanced accuracy with which they could measure phase, in this case generated through rotation. In this work, we study the rotation of ultracold bosons in an asymmetric trapping potential beyond the lowest Landau level (LLL) approximation. We demonstrate that while the LLL can identify reasonably the critical frequency for a quantum phase transition and entangled state generation, it is vital to go beyond the LLL to identify the details of the state and quantify the quantum Fisher information (which bounds the accuracy of the phase measurement). We thus identify a new parameter regime for useful entangled state generation, amenable to experimental investigation.
We present the first exact diagonalisation study of a rotating Bose-Einstein condensate stirred by a quadratic anisotropic potential near the threshold of the first vortex nucleation beyond the lowest Landau level (LLL) approximation.
Although the nucleation of the first vortex in this system has been the focus of extensive experimental and theoretical research in both mean-field studies, as well as in exact diagonalisation ones, they have all relied on the assumption of the interaction strength being weak
enough so that the system is well described by the LLL approximation. The LLL approximation accurately predicts the rotation frequency at which the first vortex penetrates the gas, and correctly describes the appearance of a quantum phase transition at a critical rotation
frequency c, which leads to quantum correlations between the atoms and entanglement in the ground state at
c.
However, our research shows that the LLL approximation fails at describing the details of the entangled state and the quantum Fisher information, which bounds the accuracy of phase measurements in metrology schemes, even for weak interactions. Our results reveal a rich system that allows for the engineering of different promising entangled states for quantum metrology, which are also amenable to
experimental investigation.
Finally, we propose an inteferometric scheme that makes use of these entangled states, which is shown to have the potential of delivering nearly Heisenberg-limited precision for the measurement of small rotations. The scheme is conceptually very simple, and it is also within
reach of current experimental technologies.
A promising practical application of entanglement is metrology, where quantum states can be used to make measurements beyond the shot noise limit. Here we consider how metrology schemes could be realised using atomic Bose-Einstein condensates (BECs) trapped in different potentials. In particular, we show that if a trapped BEC is rotated at just the right frequency, it can undergo a quantum phase transition characterised by large-scale entanglement spreading across the system. This simple process of stirring can generate interesting quantum states such as macroscopic superpositions of all the atoms flowing in opposite directions around a ring-shaped potential. We consider different trapping potentials and show how this leads to different entangled states. In particular, we find that by reducing the dimensionality of the system to one or two dimensions, it is possible to generate entangled states that are remarkably robust to the loss of atoms and so are ideally suited to precision measurement schemes.
Entanglement lies at the core of emergent quantum technologies such as quantum-enhanced metrology, quantum communication and cryptography, and quantum simulation and computing. Spinor Bose-Einstein condensates (BECs) offer a promising platform for the generation and application of entangled states. For example, a spin-1 BEC has served for the proof-of-principle demonstration of a quantum-enhanced atomic clock. Ferromagnetic spin-1 BECs with zero magnetization exhibit three ground-state quantum phases with different entanglement properties. The control parameter can be tuned by a magnetic field or by microwave dressing. As already experimentally demonstrated, an entangled ground state can be reached from a well accessible, non-entangled one by driving the control parameter across quantum phase transitions (QPTs). We investigate which of the entangled ground states afford quantum-enhanced interferometry. The interferometric usefulness is quantified by the quantum Fisher information (QFI), which we analyze throughout all ground-state phases. A large QFI at about half the Heisenberg limit, and thus far above the standard quantum limit, is attained by the well-known Twin-Fock state and by the central broken-axisymmetry (CBA) state. We detail how the CBA state can be used as a probe for quantum-enhanced interferometry. Furthermore, we observe that the large QFI of the CBA state can be traced back to enclosed macroscopic superposition states (MSSs). Measuring the atom number in one out of three modes generates, with high probability and heralded by the measurement outcome, a MSS similar to a NOON state. Our proposal promises NOON-like MSSs of unprecedentedly many atoms. Both proposed applications of the adiabatically prepared CBA state depend only on existent technology. Our numerical results show that they tolerate a reasonably swift quasiadiabatic passage in the presence of atom loss as well as uncertainties of atom counting. Excited-state quantum phase transitions (ESQPTs) extend the concept of QPTs beyond the ground state. While they have been extensively investigated theoretically, there are only few experimental results. From the perspective of quantum-state engineering, it is furthermore surprising how rarely order parameters of ESQPTs are discussed in the literature. Mean-field models for spinor BECs imply ESQPTs, to which some experimental observations on the mean-field dynamics can be attributed. However, so far, neither theoretical nor experimental studies have specifically addressed ESQPTs in spinor BECs. We extend the ground-state phase diagram of ferromagnetic spin-1 BECs with zero magnetization across the spectrum. There are three excited-state phases, corresponding to one ground-state phase each. The ESQPTs are signaled by a diverging density of states. The mean-field phase-space trajectories can be characterized by a winding number that is in one-to-one correspondence to the excited-state phases. We derive a closely related order parameter encoded in the dynamics of coherent states and discuss how this order parameter can be interferometrically measured in current experiments. Remarkably, the mean-field model governing the ESQPTs in spin-1 BECs with zero magnetization is encountered also, e. g., in molecular and nuclear physics. Because of the superior experimental control, spinor BECs can be considered as simulators of the ESQPTs in those systems. Our results contribute to quantum-state engineering and quantum-enhanced interferometry in spinor BECs and to the characterization of excited-state quantum phases. The latter may, in turn, lead on to applications in quantum-state engineering.
By considering matter wave bright solitons from weakly coupled Bose-Einstein condensates trapped in a double-well potential, we study the formation of macroscopic non-classical states, including Schrödinger-cat superposition states and maximally path entangled N00N-states. We examine Mach- Zehnder interferometer in the context of parity measurements, in order to obtain Heisenberg limit accuracy for linear phase shift measurement. We reveal that the ratio between two-body scattering length and intra-well hopping parameter can be measured with the scaling beyond this limit by using nonlinear phase shift with interacting quantum solitons.
Considering matter wave bright solitons from weakly coupled Bose-Einstein condensates trapped in a double-well potential, we study the formation of macroscopic non-classical states, including Schrödinger-cat superposition state and maximally path entangled N00N-state. We examine these macroscopic states by Mach-Zehnder interferometer in the context of parity measurements, which has been done to obtain Heisenberg limit accuracy for linear phase shift measurement. We reveal that the ratio of two-body scattering length to intra-well hopping parameter can be measured with the scaling beyond this limit by using nonlinear phase shift with interacting quantum solitons.