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Papers by Ferdinand Schmidt-Kaler
Physical Review Letters, 2008
We propose a scheme to investigate the nonequilibrium work distribution of a quantum particle und... more We propose a scheme to investigate the nonequilibrium work distribution of a quantum particle under well controlled transformations of the external potential, exploiting the versatility of a single ion in a segmented linear Paul trap. We describe in detail how the motional quantum state of a single ion can be prepared, manipulated and finally read out to fully determine the free energy difference in both harmonic and anharmonic potentials. Uniquely to our system, we show how an ion may be immersed in an engineered laser--field reservoir. Trapped ions therefore represent an ideal tool for investigating the Jarzynski equality in open and closed quantum systems.
New Journal of Physics, 2010
We focus down an ion beam consisting of single 40Ca+ ions to a spot size of a few mum using an ei... more We focus down an ion beam consisting of single 40Ca+ ions to a spot size of a few mum using an einzel-lens. Starting from a segmented linear Paul trap, we have implemented a procedure which allows us to deterministically load a predetermined number of ions by using the potential shaping capabilities of our segmented ion trap. For single-ion loading, an efficiency of 96.7(7)% has been achieved. These ions are then deterministically extracted out of the trap and focused down to a 1sigma-spot radius of (4.6 \pm 1.3)mum at a distance of 257mm from the trap center. Compared to former measurements without ion optics, the einzel-lens is focusing down the single-ion beam by a factor of 12. Due to the small beam divergence and narrow velocity distribution of our ion source, chromatic and spherical aberration at the einzel-lens is vastly reduced, presenting a promising starting point for focusing single ions on their way to a substrate.
Physical Review A, 2009
We present schemes to prepare two-dimensional cluster states [H. J. Briegel and R. Raussendorf, P... more We present schemes to prepare two-dimensional cluster states [H. J. Briegel and R. Raussendorf, Phys. Rev. Lett. {\bf 86}, 910 (2001)] with atomic ions confined in a micro-structured linear ion trap and coupled by an engineered spin-spin interaction. In particular, we show how to prepare a ntimes2n \times 2ntimes2 cluster state by creating a linear cluster state and adding third-neighbor entanglement using selective recoupling techniques. The scheme is based on the capabilities provided by segmented linear Paul traps to confine ions in local potential wells and to separate and transport ions between these wells. Furthermore, we consider creating 3 and 4-qubit cluster states by engineering the coupling matrix such that through the periodicity of the time evolution unwanted couplings are canceled. All entangling operations are achieved by switching of voltages and currents, and do not require interaction with laser light.
Protein Science, 2006
Single ions held in linear Paul traps are promising candidates for a future quantum computer. Her... more Single ions held in linear Paul traps are promising candidates for a future quantum computer. Here, we discuss a two-layer microstructured segmented linear ion trap. The radial and axial potentials are obtained from numeric field simulations and the geometry of the trap is optimized. As the trap electrodes are segmented in the axial direction, the trap allows the transport of ions between different spatial regions. Starting with realistic numerically obtained axial potentials, we optimize the transport of an ion such that the motional degrees of freedom are not excited, even though the transport speed far exceeds the adiabatic regime. In our optimization we achieve a transport within roughly two oscillation periods in the axial trap potential compared to typical adiabatic transports that take of the order 100 oscillations. Furthermore heating due to quantum mechanical effects is estimated and suppression strategies are proposed.
Physical Review Letters, 2010
We observe the phase space trajectory of an entangled wave packet of a trapped ion with high prec... more We observe the phase space trajectory of an entangled wave packet of a trapped ion with high precision. The application of a spin dependent light force on a superposition of spin states allows for coherent splitting of the matter wave packet such that two distinct components in phase space emerge. We observe such motion with a precision of better than 9% of the wave packet extension in both momentum and position, corresponding to a 0.8 nm position resolution. We accurately study the effect of the initial ion temperature on the quantum entanglement dynamics. Furthermore, we map out the phonon distributions throughout the action of the displacement force. Our investigation shows corrections to simplified models of the system evolution. The precise knowledge of these dynamics may improve quantum gates for ion crystals and lead to entangled matter wave states with large displacements.
Journal of Modern Optics, 2009
Using a segmented ion trap with mK laser-cooled ions we have realised a novel single ion source w... more Using a segmented ion trap with mK laser-cooled ions we have realised a novel single ion source which can deterministically deliver a wide range of ion species, isotopes or ionic molecules [Schnitzler et al., Phys. Rev. Lett. 102, 070501 (2009)]. Experimental data is discussed in detail and compared with numerical simulations of ion trajectories. For the novel ion source we investigate numerically the influence of various extraction parameters on fluctuations in velocity and position of the beam. We present specialized ion optics and show from numerical simulations that nm resolution is achievable. The Paul trap, which is used as a single ion source, together with the presented ion optics, constitutes a promising candidate for a deterministic ion implantation method for applications in solid state quantum computing or classical nano-electronic devices.
We investigate experimentally quantum information processing using a string of trapped ions where... more We investigate experimentally quantum information processing using a string of trapped ions where each ion represents a bit of quantum information (qubit). We report on the realization of the Cirac Zoller universal control-NOT gate with a two-ion crystal. Quantum gates between the ions are realized by coupling them through their collective quantized motion. We show that the control ion's qubit state determines the evolution of the target ion's qubit state. Additionally, we report on a tomographic method to fully characterize the quantum state of a qubit register. Using this tomographic method we investigate Bell states which we generate in a two-qubit system and quantify their entanglement.
Applied Physics B-lasers and Optics, 2010
We introduce a measurement scheme that utilizes a single ion as a local field probe. The ion is c... more We introduce a measurement scheme that utilizes a single ion as a local field probe. The ion is confined in a segmented Paul trap and shuttled around to reach different probing sites. By the use of a single atom probe, it becomes possible characterizing fields with spatial resolution of a few nm within an extensive region of millimeters. We demonstrate the scheme by accurately investigating the electric fields providing the confinement for the ion. For this we present all theoretical and practical methods necessary to generate these potentials. We find sub-percent agreement between measured and calculated electric field values.
Physical Review Letters, 1992
We have compared the frequency of the hydrogen 1S-2S transition (resonance width Deltanu/nu=2.8×1... more We have compared the frequency of the hydrogen 1S-2S transition (resonance width Deltanu/nu=2.8×10-11) with a reference frequency synthesized from an 88-THz infrared CH4-stabilized HeNe laser. In this first measurement of an optical frequency that overcomes the uncertainty limits of the visible I2-stabilized He-Ne laser standard, we find a 1S-2S frequency of 2 466 061 413.182(45) MHz with an 18-fold improved
New Journal of Physics, 2008
We use a single ion as an movable electric field sensor with accuracies on the order of a few V/m... more We use a single ion as an movable electric field sensor with accuracies on the order of a few V/m. For this, we compensate undesired static electric fields in a planar RF trap and characterize the static fields over an extended region along the trap axis. We observe a strong buildup of stray charges around the loading region on the trap resulting in an electric field of up to 1.3 kV/m at the ion position. We also find that the profile of the stray field remains constant over a time span of a few months.
In an experiment with a single trapped barium ion we demonstrate that a laser-excited atom whose ... more In an experiment with a single trapped barium ion we demonstrate that a laser-excited atom whose surrounding electromagnetic vacuum field is modified by a distant mirror experiences vacuum-induced forces which notably change its trapping conditions.
Physical Review Letters, 2004
Physical Review Letters, 1999
A single Ca+ ion in a Paul trap has been cooled to the ground state of vibration with up to 99.9%... more A single Ca+ ion in a Paul trap has been cooled to the ground state of vibration with up to 99.9% probability. Starting from this Fock state |n=0> we have demonstrated coherent quantum state manipulation on an optical transition. Up to 30 Rabi oscillations within 1.4 ms have been observed. We find a similar number of Rabi oscillations after preparation of the ion in the |n=1> Fock state. The coherence of optical state manipulation is only limited by laser and ambient magnetic field fluctuations. Motional heating has been measured to be as low as one vibrational quantum in 190 ms.
Physical Review Letters, 2004
Physical Review Letters, 2008
We propose a scheme to investigate the nonequilibrium work distribution of a quantum particle und... more We propose a scheme to investigate the nonequilibrium work distribution of a quantum particle under well controlled transformations of the external potential, exploiting the versatility of a single ion in a segmented linear Paul trap. We describe in detail how the motional quantum state of a single ion can be prepared, manipulated and finally read out to fully determine the free energy difference in both harmonic and anharmonic potentials. Uniquely to our system, we show how an ion may be immersed in an engineered laser--field reservoir. Trapped ions therefore represent an ideal tool for investigating the Jarzynski equality in open and closed quantum systems.
New Journal of Physics, 2010
We focus down an ion beam consisting of single 40Ca+ ions to a spot size of a few mum using an ei... more We focus down an ion beam consisting of single 40Ca+ ions to a spot size of a few mum using an einzel-lens. Starting from a segmented linear Paul trap, we have implemented a procedure which allows us to deterministically load a predetermined number of ions by using the potential shaping capabilities of our segmented ion trap. For single-ion loading, an efficiency of 96.7(7)% has been achieved. These ions are then deterministically extracted out of the trap and focused down to a 1sigma-spot radius of (4.6 \pm 1.3)mum at a distance of 257mm from the trap center. Compared to former measurements without ion optics, the einzel-lens is focusing down the single-ion beam by a factor of 12. Due to the small beam divergence and narrow velocity distribution of our ion source, chromatic and spherical aberration at the einzel-lens is vastly reduced, presenting a promising starting point for focusing single ions on their way to a substrate.
Physical Review A, 2009
We present schemes to prepare two-dimensional cluster states [H. J. Briegel and R. Raussendorf, P... more We present schemes to prepare two-dimensional cluster states [H. J. Briegel and R. Raussendorf, Phys. Rev. Lett. {\bf 86}, 910 (2001)] with atomic ions confined in a micro-structured linear ion trap and coupled by an engineered spin-spin interaction. In particular, we show how to prepare a ntimes2n \times 2ntimes2 cluster state by creating a linear cluster state and adding third-neighbor entanglement using selective recoupling techniques. The scheme is based on the capabilities provided by segmented linear Paul traps to confine ions in local potential wells and to separate and transport ions between these wells. Furthermore, we consider creating 3 and 4-qubit cluster states by engineering the coupling matrix such that through the periodicity of the time evolution unwanted couplings are canceled. All entangling operations are achieved by switching of voltages and currents, and do not require interaction with laser light.
Protein Science, 2006
Single ions held in linear Paul traps are promising candidates for a future quantum computer. Her... more Single ions held in linear Paul traps are promising candidates for a future quantum computer. Here, we discuss a two-layer microstructured segmented linear ion trap. The radial and axial potentials are obtained from numeric field simulations and the geometry of the trap is optimized. As the trap electrodes are segmented in the axial direction, the trap allows the transport of ions between different spatial regions. Starting with realistic numerically obtained axial potentials, we optimize the transport of an ion such that the motional degrees of freedom are not excited, even though the transport speed far exceeds the adiabatic regime. In our optimization we achieve a transport within roughly two oscillation periods in the axial trap potential compared to typical adiabatic transports that take of the order 100 oscillations. Furthermore heating due to quantum mechanical effects is estimated and suppression strategies are proposed.
Physical Review Letters, 2010
We observe the phase space trajectory of an entangled wave packet of a trapped ion with high prec... more We observe the phase space trajectory of an entangled wave packet of a trapped ion with high precision. The application of a spin dependent light force on a superposition of spin states allows for coherent splitting of the matter wave packet such that two distinct components in phase space emerge. We observe such motion with a precision of better than 9% of the wave packet extension in both momentum and position, corresponding to a 0.8 nm position resolution. We accurately study the effect of the initial ion temperature on the quantum entanglement dynamics. Furthermore, we map out the phonon distributions throughout the action of the displacement force. Our investigation shows corrections to simplified models of the system evolution. The precise knowledge of these dynamics may improve quantum gates for ion crystals and lead to entangled matter wave states with large displacements.
Journal of Modern Optics, 2009
Using a segmented ion trap with mK laser-cooled ions we have realised a novel single ion source w... more Using a segmented ion trap with mK laser-cooled ions we have realised a novel single ion source which can deterministically deliver a wide range of ion species, isotopes or ionic molecules [Schnitzler et al., Phys. Rev. Lett. 102, 070501 (2009)]. Experimental data is discussed in detail and compared with numerical simulations of ion trajectories. For the novel ion source we investigate numerically the influence of various extraction parameters on fluctuations in velocity and position of the beam. We present specialized ion optics and show from numerical simulations that nm resolution is achievable. The Paul trap, which is used as a single ion source, together with the presented ion optics, constitutes a promising candidate for a deterministic ion implantation method for applications in solid state quantum computing or classical nano-electronic devices.
We investigate experimentally quantum information processing using a string of trapped ions where... more We investigate experimentally quantum information processing using a string of trapped ions where each ion represents a bit of quantum information (qubit). We report on the realization of the Cirac Zoller universal control-NOT gate with a two-ion crystal. Quantum gates between the ions are realized by coupling them through their collective quantized motion. We show that the control ion's qubit state determines the evolution of the target ion's qubit state. Additionally, we report on a tomographic method to fully characterize the quantum state of a qubit register. Using this tomographic method we investigate Bell states which we generate in a two-qubit system and quantify their entanglement.
Applied Physics B-lasers and Optics, 2010
We introduce a measurement scheme that utilizes a single ion as a local field probe. The ion is c... more We introduce a measurement scheme that utilizes a single ion as a local field probe. The ion is confined in a segmented Paul trap and shuttled around to reach different probing sites. By the use of a single atom probe, it becomes possible characterizing fields with spatial resolution of a few nm within an extensive region of millimeters. We demonstrate the scheme by accurately investigating the electric fields providing the confinement for the ion. For this we present all theoretical and practical methods necessary to generate these potentials. We find sub-percent agreement between measured and calculated electric field values.
Physical Review Letters, 1992
We have compared the frequency of the hydrogen 1S-2S transition (resonance width Deltanu/nu=2.8×1... more We have compared the frequency of the hydrogen 1S-2S transition (resonance width Deltanu/nu=2.8×10-11) with a reference frequency synthesized from an 88-THz infrared CH4-stabilized HeNe laser. In this first measurement of an optical frequency that overcomes the uncertainty limits of the visible I2-stabilized He-Ne laser standard, we find a 1S-2S frequency of 2 466 061 413.182(45) MHz with an 18-fold improved
New Journal of Physics, 2008
We use a single ion as an movable electric field sensor with accuracies on the order of a few V/m... more We use a single ion as an movable electric field sensor with accuracies on the order of a few V/m. For this, we compensate undesired static electric fields in a planar RF trap and characterize the static fields over an extended region along the trap axis. We observe a strong buildup of stray charges around the loading region on the trap resulting in an electric field of up to 1.3 kV/m at the ion position. We also find that the profile of the stray field remains constant over a time span of a few months.
In an experiment with a single trapped barium ion we demonstrate that a laser-excited atom whose ... more In an experiment with a single trapped barium ion we demonstrate that a laser-excited atom whose surrounding electromagnetic vacuum field is modified by a distant mirror experiences vacuum-induced forces which notably change its trapping conditions.
Physical Review Letters, 2004
Physical Review Letters, 1999
A single Ca+ ion in a Paul trap has been cooled to the ground state of vibration with up to 99.9%... more A single Ca+ ion in a Paul trap has been cooled to the ground state of vibration with up to 99.9% probability. Starting from this Fock state |n=0> we have demonstrated coherent quantum state manipulation on an optical transition. Up to 30 Rabi oscillations within 1.4 ms have been observed. We find a similar number of Rabi oscillations after preparation of the ion in the |n=1> Fock state. The coherence of optical state manipulation is only limited by laser and ambient magnetic field fluctuations. Motional heating has been measured to be as low as one vibrational quantum in 190 ms.
Physical Review Letters, 2004