Spectroscopy of interacting quasiparticles

Spectroscopy of interacting quasiparticles in trapped ions.
P. Jurcevic, P. Hauke, C. Maier, C. Hempel, B. P. Lanyon, R. Blatt, C. F. Roos.
Phys. Rev. Lett. 115, 100501 (2015)
arXiv version: PDF

There is currently a large research endeavour to couple together precisely-controllable quantum systems, to form engineered quantum many-body systems. Such systems are of interest for e.g. enhanced-measurements, computation and to study quantum many-body physics. Prominent approaches include the use of atoms in optical lattices, ions in electric traps and superconducting circuits. As these engineered systems become larger and more complex, new methods are required to characterise them: to determine what has been built in the laboratory and to study their emergent phenomena.

In our paper we present and demonstrate a technique for performing spectroscopy of an engineered quantum-many body system. Our work complements and extends recent work on translating spectroscopic techniques for natural systems, to the engineered case (e.g. [1, 2]). In particular, we exploit the ability to individually manipulate and measure the system’s individual constituent particles. This control allows us to resolve new engineered quantum phenomena for the first time, via their spectral signature.

We use our technique to study an interacting system of trapped atomic-ions [3], that is well described by a model of interacting quantum spins. Using laser beams which couple the internal states of the 40Ca+ ions to all transverse vibrational modes of the ion string, we engineer an interaction which can be described by a long-range Ising model in a strong transverse field. By exciting the system into close approximations of many-body spin waves, and observing the site-resolved dynamical response, we are able to characterise the system’s emergent quasiparticle excitations. First, we extract the quasiparticle dispersion relationship, responsible for the distribution of information and correlations in the system [3, 4, 5]. Second, we resolve spectral shifts due to quasiparticle scattering, and thereby confirm that models of non-interacting bosons or fermions cannot describe our system.

 
  quasiparticle spectroscopy Figure 1 - Magnetization dynamics in 7-ion string prepared in an approximate superposition of eigenstates. The left column shows spectroscopy of a superposition of the ground state with a spin wave state, the right column experimens with a superposition of two spin wave states. For further details see text.

The data in the figure show two kinds of single-quasi-particle spectroscopy experiments. We superpose either an approximate spin wave state with the ground state or with another spin wave state and let the system evolve under the Ising dynamics. The resulting magnetization dynamics is well described by a single frequency which can be obtained by summing up the single-ion magnetization signals Mi(t)  in a suitable way and taking their Fourier transform.
 
By means of these measurements, we can extract the energy of the spin wave states with respect to the energy of the ground state in which all spins are aligned with the transverse field.
 
 In a set of further experiments we created exactly two quasiparticles which belong to either of two quasiparticle modes and carried out a similar experiment in which we measured spin-spin correlations as a function of time. Due to quasiparticle interactions the spectra become much richer and show that the quasiparticles of our system cannot be described by non-ineracting bosons or by non-interacting fermions (as would be the case for an Ising model with nearest-neighbour interactions only).
 
We anticipate that our technique will find application well beyond trapped-ion experiments, and that our results will be of interest to the broad range of physicists working on engineered quantum systems.
 

Literature

 

  1. M. Knap et al., Probing Real-Space and Time-Resolved Correlation Functions with Many-Body Ramsey Interferometry, Phys. Rev. Lett. 111, 147205 (2013).
  2. C. Senko et al, Coherent imaging spectroscopy of a quantum many-body spin system. Science 345, 430 (2014).
  3. P. Jurcevic et al., Quasiparticle engineering and entanglement propagation in a quantum many-body system. Nature 511, 202 (2014).
  4. M. Cheneau et al., Light-cone-like spreading of correlations in a quantum many-body system. Nature 481, 484 (2012).
  5. P. Richerme et al., Non-local propagation or correlations of correlations in long-range interacting quantum systems. Nature 511,198 (2014).

Financial support

This research was supported by the Austrian Academy of Science, the University of Innsbruck, the Austrian Science Fund FWF and by the European Commission via the integrated project SIQS and the Institut für Quanteninformation GmbH.
CR, Sept 2015