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arXiv:quant-ph/0603129 · Physical Review Letters

Adiabatic Mach-Zehnder Interferometry on a Quantized Bose-Josephson Junction

Chaohong Lee

Published Oct 10, 2006• 131 citations
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Abstract

We propose a scheme to achieve Mach-Zehnder interferometry using a quantized Bose-Josephson junction with a negative charging energy. The quantum adiabatic evolution through a dynamical bifurcation is used to accomplish the beam splitting and recombination. The negative charging energy ensures the existence of a path-entangled state which enhances the phase measurement precision to the Heisenberg limit. A feasible detection procedure is also presented. The scheme should be realizable with current technology.

DOI
10.1103/physrevlett.97.150402

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We propose a scheme to achieve Mach-Zehnder interferometry using a quantized Bose-Josephson junction with a negative charging energy. The quantum adiabatic evolution through a dynamical bifurcation is used to accomplish the beam splitting and recombination. The negative charging energy ensures the existence of a path-entangled state which enhances the phase measurement precision to the Heisenberg limit. A feasible detection procedure is also presented. The scheme should be realizable with current technology.
Mach-Zehnder interferometer, a powerful tool for a wide variety of measurements, has been realized with Bose-Einstein condensates in recent experiments. In this report, we propose and analyze a realizable scheme for performing a Heisenberg-limited Mach-Zehnder interferometry with dipolar spin-1 condensate. Based upon adiabatic processes of sweeping the transverse magnetic field, we demonstrate a perfect phase transition, which accomplishes the beam splitter, phase shifter and recombiner as for a Mach-Zehnder interferometer. The attractive dipolar interaction ensures the existence of a path-entangled state which enhances the phase measurement precision to the Heisenberg limit. We also discuss the spin-111 squeezing induced in the adiabatic passage and show that the squeezing parameter attains its minimal value near the point of saturation field.
We propose a scheme to realize high-precision quantum interferometry with entangled non-Gaussian states by driving the system through quantum phase transitions. The beam splitting, in which an initial nondegenerate ground state evolves into a highly entangled state, is achieved by adiabatically driving the system from a nondegenerate regime to a degenerate one. Inversely, the beam recombination, in which the output state after interrogation becomes gradually disentangled, is accomplished by adiabatically driving the system from the degenerate regime to the nondegenerate one. The phase shift, which is accumulated in the interrogation process, can then be easily inferred via population measurement. We apply our scheme to Bose condensed atoms and trapped ions and find that Heisenberg-limited precision scalings can be approached. Our proposed scheme does not require single-particle resolved detection and is within the reach of current experiment techniques.
We propose a scheme to realize high-precision many-body quantum interferometry by driving the system through quantum phase transitions. The beam splitting, in which an initial non-degenerate groundstate evolves into a highly entangled state, is achieved by adiabatically driving the system from a non-degenerate regime to a degenerate one. Inversely, the beam recombination, in which the output state after interrogation becomes gradually disentangled, is accomplished by adiabatically driving the system from the degenerate regime to the non-degenerate one. The phase shift, which is accumulated in the interrogation process, can then be easily inferred via population measurement. We apply our scheme to two-mode Bose condensed atoms and spin-1 Bose-Einstein condensates, and find that Heisenberg-limited precision scalings can be approached. Our proposed scheme does not require single-particle resolved detection and is within the reach of current experiment techniques.
In a two-mode Bose-Josephson junction the dynamics induced by a sudden quench of the tunnel amplitude leads to the periodic formation of entangled states. For instance, squeezed states are formed at short times and macroscopic superpositions of phase states at later times. In atom interferometry, the two modes of the junction play the role of the two arms of a Mach-Zehnder interferometer; use of multiparticle entangled states allows the enhancement of phase sensitivity with respect to that obtained from uncorrelated atoms. Decoherence due to the presence of noise degrades quantum correlations between atoms, thus reducing phase sensitivity. We consider decoherence due to stochastic fluctuations of the energies of the two modes of the junction. We analyze its effect on squeezed states and macroscopic superpositions and calculate the squeezing parameter and the quantum Fisher information during the quenched dynamics. The latter quantity measures the amount of quantum correlations useful in interferometry. For moderate noise intensities, we show that it increases on time scales beyond the squeezing regime. This suggests multicomponent superpositions of phase states as interesting candidates for high-precision atom interferometry.
Abstract The coherent manipulation of a quantum wave is at the core of quantum sensing. For instance, atom interferometers require linear splitting and recombination processes to map the accumulated phase shift into a measurable population signal. Although Bose Einstein condensates (BECs) are the archetype of coherent matter waves, their manipulation between trapped spatial modes has been limited by the strong interparticle collisions. Here, we overcome this problem by using BECs with tunable interaction trapped in an innovative array of double-well potentials and exploiting quantum tunneling to realize linear beam splitting. We operate several Mach-Zehnder interferometers in parallel, canceling common-mode potential instabilities by a differential analysis, thus demonstrating a trapped-atom gradiometer. Furthermore, by applying a spin-echo protocol, we suppress additional decoherence sources and approach unprecedented coherence times of one second. Our interferometer will find applications in precision measurements of forces with a high spatial resolution and in linear manipulation of quantum entangled states for sensing with sub shot-noise sensitivity.
Particle-wave duality enables the construction of interferometers for matter waves, which complement optical interferometers in precision measurement devices. This requires the development of atom-optics analogues to beam splitters, phase shifters and recombiners. Integrating these elements into a single device has been a long-standing goal. Here we demonstrate a full Mach–Zehnder sequence with trapped Bose–Einstein condensates confined on an atom chip. Particle interactions in our Bose–Einstein condensate matter waves lead to a nonlinearity, absent in photon optics. We exploit it to generate a non-classical state having reduced number fluctuations inside the interferometer. Making use of spatially separated wave packets, a controlled phase shift is applied and read out by a non-adiabatic matter-wave recombiner. We demonstrate coherence times a factor of three beyond what is expected for coherent states, highlighting the potential of entanglement as a resource for metrology. Our results pave the way for integrated quantum-enhanced matter-wave sensors. Atom interferometers exploit wave-particle duality and can be used as sensitive measurement devices. Berrada et al.present a Mach–Zehnder interferometer for Bose–Einstein condensates trapped on an atom chip and demonstrate enhanced performance using non-classical states.