We study phonons in a dynamical chain of ions confined by a trap with a time-dependent (axial) potential strength and demonstrate that they behave in the same way as quantum fields in an expanding or contracting Universe. Based on this analogy, we present a scheme for the detection of the analogue of cosmological particle creation which should be feasible with present day technology. In order to test the quantum nature of the particle creation mechanism and to distinguish it from classical effects such as heating, we propose to measure the two-phonon amplitude via the 2nd red sideband transition and to compare it with the one-phonon amplitude (1st red sideband).
We study phonons in a dynamical chain of ions confined by a trap with a time-dependent (axial) potential strength and demonstrate that they behave in the same way as quantum fields in an expanding or contracting Universe. Based on this analogy, we present a scheme for the detection of the analogue of cosmological particle creation which should be feasible with present day technology. In order to test the quantum nature of the particle creation mechanism and to distinguish it from classical effects such as heating, we propose to measure the two-phonon amplitude via the 2nd red sideband transition and to compare it with the one-phonon amplitude (1st red sideband).
We consider the transversal modes of ions in a linear radio-frequency trap where we control the time-dependent axial confinement to show that we can excite quanta of motion via a two-mode squeezing process. This effect is analogous to phenomena predicted to occur in the early universe, in general out of reach for experimental investigation. As a substantial advantage of this proposal in comparison to previous ones we propose to exploit the radial and axial modes simultaneously to permit experimental access of these effects based on state-of-the-art technology. In addition, we propose to create and explore entanglement between the two ions.
Quantum theory predicts intriguing dynamics during drastic changes of external conditions. We switch the trapping field of two ions sufficiently fast to tear apart quantum fluctuations, i.e., create pairs of phonons and, thereby, squeeze the ions' motional state. This process can be interpreted as an experimental analog to cosmological particle creation and is accompanied by the formation of spatial entanglement. Hence, our platform allows one to study the causal connections of squeezing, pair creation, and entanglement and might permit one to cross-fertilize between concepts in cosmology and applications of quantum information processing.
The fundamental laws of quantum mechanics are far from our everyday life experiences. However, they have been extremely successful in explaining observations in microscopic physical systems and are, already, harnessed for several applications. Moreover, in combination with relativistic considerations, basic phenomena from quantum mechanics are accredited a central role in the (macroscopic) evolution of our universe. In this thesis, we employ a trapped ion quantum simulator to experimentally investigate two fundamental quantum mechanical effects that have been extensively studied for many decades. In the first investigation, we implement non-adiabatic changes of the ions’ trapping potential in order to amplify quantum vacuum fluctuations. Following theoretical works by others, this mechanism can be interpreted as an analog to the creation of particles during cosmic inflation in the early universe. Such cosmological particles are considered as the seeds for the formation of the large-scale structures in our universe that we observe nowadays. In our analog quantum simulation, the creation of particles is evidenced by the detection of a squeezed state in the motion of the ions. A remarkable feature of this mechanism is the accompanying creation of quantum entanglement. In case of the cosmological particles, this entanglement spreads over large, cosmic distances. In the second investigation, we benchmark a theoretical concept in the framework of open quantum systems in a most basic system and under near-ideal conditions. In nature, any quantum system inevitably interacts with its environment and, thereby, needs ultimately to be considered an open system that can build up correlations and, even, entanglement with its environment. We implement a spin-1/2 system in the electronic degree of freedom of a single trapped ion, which we couple to a bosonic environment, formed by a motional degree of freedom of the ion. Further, we implement a tunable interaction between system and environment that, in turn, can lead to entanglement. By performing measurements on the open system only, we observe quantum non-Markovian behavior, which we quantify using a rigorously defined measure. Thereby, we reveal that the quantification of such quantum memory effects is fundamentally limited by fundamental quantum mechanical measurement uncertainties. The investigations presented in this thesis significantly expand the capabilities of our trapped ion platform to perform analog quantum simulations of fundamental quantum mechanical problems under near-ideal conditions, and enable future studies of increased complexity and under more realistic conditions.
In standard cosmological models, inflation is driven by a quantum field, the inflaton, whos constant energy density drove the superluminal expansion of the universe [1]. When inflation stops, the universe has an extremely low density btu the inflaton field starts to oscillate arround its minimum of energy and decays into entengled pairs of particles [2], known as the pre-heating phase. Created pairs of particles then start to interact leading to decoherence and thermalization : the re-heating stage. If in situ observation of inflaton particle creation process is impossible, this pair production through parametric amplification is analogous to the creation of phonon pairs in a Bose-Einstein (BEC) condensate whose interaction strenght is time modulated. Modulating the stiffness of a dipole trap of a cigar-shape BEC being equivalent to modulate the effective one-dimensionnal interaction strenght in a BEC, we are able to probe the correlation of entengled metastable helium atoms by the use of a micro-channel plate detector (MCP). Our experimental procedure is the following [3] : we modulate in time the trap stiffness of the dipole trap laser and then release the trap (see figure 1). During expansion, the phonon kinetic energy is adiabatically transferred to one atom that is detected by the MCP after a 300 ms time of flight. The amount of created phonon pairs is expected to depend on the duration of the excitation, its amplitude and the excitation frequency. However, the region in which the entenglement of the phonon pairs can be observed is expected to be quite narrow [4]. We propose to investigate the entenglement and correlations of those pairs of particles. [1] L. Kofman, A. Linde, and A. Starobinsky, Phys. Rev. D 56, 3258 (1997). [2] D. Campo and R. Parentani, Phys. Rev. D 74, 025001 (2006). [3] S. Robertson, F. Michel, and R. Parentani, Phys. Rev. D 95, 065020 (2017). [4] J.-C. Jaskula et al., Phys. Rev. Lett. 109, 220401 (2012).
We show that a variety of cosmologically motivated effective quasiparticle space-times can be produced in harmonically trapped superfluid Bose and Fermi gases. We study the analog of cosmological particle production in these effective space-times, induced by trapping potentials and coupling constants possessing an arbitrary time dependence. The WKB probabilities for phonon creation from the superfluid vacuum are calculated, and an experimental procedure to detect quasiparticle production by measuring density-density correlation functions is proposed.
Driving an ion at a motional sideband transition induces the Jaynes--Cummings (JC) interaction. This JC interaction creates an anharmonic ladder of JC eigenstates, resulting in the suppression of phonon hopping due to energy conservation. Here, we report the confinement of multiple local phonons to a single ion site using this nonlinear quantum effect. By using phonon-number-resolving detection, we observe the dynamics of multiple phonons in an ion chain. In addition to simply confining local phonons, by turning the JC interaction on and off dynamically, we can confine a single local phonon to a single ion site and subsequently retrieve it out of the site. Our work establishes a key technological component for quantum simulation with multiple bosonic particles, which can simulate classically intractable problems.