A tomography of many-body quantum states of indistinguishable particles is generally performed by engineering couplings between the involved states and a subsequent counting of the occupation numbers. While precise couplings belong to the standard experimental toolbox, an accurate number counting presents a considerable challenge for both photonic and atomic quantum states. Here we present an application of a number-resolving atom counting [New J. Phys. 23, 113046 (2021)] for the state reconstruction of an atomic coherent spin state. We generate the coherent spin state by driving a Rabi frequency between two hyperfine states of an ultracold Rubidium ensemble.The result is analyzed by a number-resolving fluoresence detection setup. We characterize the fidelity of our detector and show that a negative-valued Wigner function is associated with it. The results offer an exciting perspective for a high-fidelity tomography of entangled states and can be applied for the future demonstration of Heisenberg-limited atom interferometry.
Compared to light interferometers, the flux in cold-atom interferometers is low and the associated shot noise large. Sensitivities beyond these limitations require the preparation of entangled atoms in different momentum modes. Here, we demonstrate a source of entangled atoms that is compatible with state-of-the-art interferometers. Entanglement is transferred from the spin degree of freedom of a Bose-Einstein condensate to well-separated momentum modes, witnessed by a squeezing parameter of -3.1(8) dB. Entanglement-enhanced atom interferometers open up unprecedented sensitivities for quantum gradiometers or gravitational wave detectors.
Spin changing collisions in alkaline Bose-Einstein condensates can be employed to generate highly entangled atomic quantum states. Here, we will report on the generation of two classes of entangled states. Firstly, we demonstrate the generation of two-mode squeezed vacuum states and record their characteristic quadrature correlations by atomic homodyning. We prove that the correlations fulfill Reid’s criterion [1] for continuous-variable Einstein-Podolsky-Rosen entanglement. The homodyne measurements allow for a full tomographic reconstruction, yielding a two-mode squeezed state with a 78% fidelity. The created state can be directly applied to atom interferometry, as is exemplified by an atomic clock measurement beyond the Standard Quantum Limit.
Secondly, we demonstrate entanglement between two spatially separated atomic modes. The entangled state is obtained by spatially splitting a Twin Fock state of indistinguishable atoms along a line of zero density. This structure of two separated atomic modes is obtained by utilizing an excited trap mode. The non-classical correlations between these atomic modes are verified by applying a novel entanglement criterion especially sensitive for our case. The method opens a path to exploit the recent success in the creation of many-particle entanglement in ultracold atoms for the field of quantum information, where individually addressable subsystems are required. Finally, we will show how the measurement protocol can be extended to perform a Bell test of quantum nonlocality.
[1] M. Reid, Phys. Rev. A 40, 913-923 (1989)
Since the pioneering work of Ramsey, atom interferometers are employed for precision metrology, in particular to measure time and to realize the second. In a classical interferometer, an ensemble of atoms is prepared in one of the two input states, whereas the second one is left empty. In this case, the vacuum noise restricts the precision of the interferometer to the standard quantum limit (SQL). Here, we propose and experimentally demonstrate a novel clock configuration that surpasses the SQL by squeezing the vacuum in the empty input state. We create a squeezed vacuum state containing an average of 0.75 atoms to improve the clock sensitivity of 10,000 atoms by 2.05 dB. The SQL poses a significant limitation for today's microwave fountain clocks, which serve as the main time reference. We evaluate the major technical limitations and challenges for devising a next generation of fountain clocks based on atomic squeezed vacuum.
In 1935, Einstein, Podolsky and Rosen (EPR) questioned the completeness of quantum mechanics by devising a quantum state of two massive particles with maximally correlated space and momentum coordinates. The EPR criterion qualifies such continuous-variable entangled states, as shown successfully with light fields. Here, we report on the production of massive particles which meet the EPR criterion for continuous phase/amplitude variables. The created quantum state of ultracold atoms shows an EPR parameter of 0.18(3), which is 2.4 standard deviations below the threshold of 1/4. Our state presents a resource for tests of quantum nonlocality with massive particles and a wide variety of applications in the field of continuous-variable quantum information and metrology.
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