Motion and gravity effects in the precision of quantum clocks

We show that motion and gravity affect the precision of quantum clocks. We consider a localised quantum field as a fundamental model of a quantum clock moving in spacetime and show that its state is modified due to changes in acceleration. By computing the quantum Fisher information we determine how relativistic motion modifies the ultimate bound in the precision of the measurement of time. While in the absence of motion the squeezed vacuum is the ideal state for time estimation, we find that it is highly sensitive to the motion-induced degradation of the quantum Fisher information. We show that coherent states are generally more resilient to this degradation and that in the case of very low initial number of photons, the optimal precision can be even increased by motion. These results can be tested with current technology by using superconducting resonators with tunable boundary conditions.Comment: 10 pages, 6 figures. I. F. previously published as I. Fuentes-Guridi and I. Fuentes-Schulle

Scattering of coherent pulses on a two-level system-single-photon generation

In this paper, we consider a two-level system (TLS) coupled to a one-dimensional continuum of bosonic modes in a transmission line (TL). Using the master equation approach, a method for determining the photon number distribution of the scattered field is outlined. Specifically, results for the reflected field when driving the TLS with a coherent pulse are given. While the one-photon probability is enhanced compared to the incident coherent field, the system is still not a good deterministic single-photon source. Extending the system to contain two separate TLs, however, output fields with one-photon probabilities close to unity can be reached

Twin paradox with macroscopic clocks in superconducting circuits

We propose an implementation of a twin paradox scenario in superconducting circuits, with velocities as large as a few percent of the speed of light. Ultrafast modulation of the boundary conditions for the electromagnetic field in a microwave cavity simulates a clock moving at relativistic speeds. Since our cavity has a finite length, the setup allows us to investigate the role of clock size as well as interesting quantum effects on time dilation. In particular, our theoretical results show that the time dilation increases for larger cavity lengths and is shifted due to quantum particle creation.Comment: 6 pages, 3 figures. I. F. previously published as I. Fuentes-Guridi and I. Fuentes-Schulle

Dynamical response of Bose-Einstein condensates to oscillating gravitational fields

© 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft. A description of the dynamical response of uniformly trapped Bose-Einstein condensates (BECs) to oscillating external gravitational fields is developed, with the inclusion of damping. Two different effects that can lead to the creation of phonons in the BEC are identified; direct driving and parametric driving. Additionally, the oscillating gravitational field couples phonon modes, which can lead to the transition of excitations between modes. The special case of the gravitational field of a small, oscillating sphere located closely to the BEC is considered. It is shown that measurement of the effects may be possible for oscillating source masses down to the milligram scale, with a signal to noise ratio of the order of 10. To this end, noise terms and variations of experimental parameters are discussed and generic experimental parameters are given for specific atom species. The results of this article suggest the utility of BECs as sensors for the gravitational field of very small oscillating objects which may help pave the way towards gravity experiments with masses in the quantum regime

Generation of nonclassical microwave states using an artificial atom in 1D open space

We have embedded an artificial atom, a superconducting transmon qubit, in a 1D open space and investigated the scattering properties of an incident microwave coherent state. By studying the statistics of the reflected and transmitted fields, we demonstrate that the scattered states can be nonclassical. In particular, by measuring the second-order correlation function, $g^{(2)}$, we show photon antibunching in the reflected field and superbunching in the transmitted field. We also compare the elastically and inelastically scattered fields using both phase-sensitive and phase-insensitive measurements.Comment: 5 pages, 3 figure

Quantum optics and relativistic motion with superconducting circuits

Superconducting microwave circuits provide a versatile platform for studying quantum optics with artificial atoms, mainly motivated by applications in quantum information. In addition, the circuits are promising for simulation of relativistic phenomena. This thesis is based on theoretical work along both these lines.Firstly, we consider a transmon coupled to an open transmission line. Using circuit quantization techniques and the master equation formalism, we theoretically describe scattering of coherent microwaves states on the transmon. The results agree with various recent experiments. As an example, we see a photon number redistribution leading to antibunching in the reflected field and superbunching in the transmitted field. Inspired by these results, we further investigate the possibility of generating single-photon states on demand in the system. We find that a single two-level system in an open transmission line is not a suitable single-photon source. With an asymmetric setup using two transmission lines, however, single-photon probabilities close to unity can be achieved.Secondly, we investigate simulation of a relativistically moving cavity containing a quantum field.Previously, in order to demonstrate the dynamical Casimir effect, a SQUID was used to tune a boundary condition in a way that mimics a moving mirror. Building on this idea, we extend the setup and use two SQUIDs to simulate the moving cavity. An experiment is proposed where the cavity is used as a clock and we show that time dilation should be observable for realistic circuit parameters. We also show how the size and the acceleration of the clock leads to a deviation from the ideal clock formula. Moreover, the effect of acceleration on the precision of the clock is analyzed

Quantum optics and relativistic motion with superconducting circuits

Superconducting microwave circuits provide a versatile platform for studying quantum optics with artificial atoms, mainly motivated by applications in quantum information. In addition, the circuits are promising for simulation of relativistic phenomena. This thesis is based on theoretical work along both these lines.Firstly, we consider a transmon coupled to an open transmission line. Using circuit quantization techniques and the master equation formalism, we theoretically describe scattering of coherent microwaves states on the transmon. The results agree with various recent experiments. As an example, we see a photon number redistribution leading to antibunching in the reflected field and superbunching in the transmitted field. Inspired by these results, we further investigate the possibility of generating single-photon states on demand in the system. We find that a single two-level system in an open transmission line is not a suitable single-photon source. With an asymmetric setup using two transmission lines, however, single-photon probabilities close to unity can be achieved.Secondly, we investigate simulation of a relativistically moving cavity containing a quantum field.Previously, in order to demonstrate the dynamical Casimir effect, a SQUID was used to tune a boundary condition in a way that mimics a moving mirror. Building on this idea, we extend the setup and use two SQUIDs to simulate the moving cavity. An experiment is proposed where the cavity is used as a clock and we show that time dilation should be observable for realistic circuit parameters. We also show how the size and the acceleration of the clock leads to a deviation from the ideal clock formula. Moreover, the effect of acceleration on the precision of the clock is analyzed

Simulating moving cavities in superconducting circuits

We theoretically investigate the simulation of moving cavities in a superconducting circuit setup. In particular, we consider a recently proposed experimental scenario where the phase of the cavity field is used as a moving clock. By computing the error made when simulating the cavity trajectory with SQUIDs, we identify parameter regimes where the correspondence holds, and where time dilation, as well as corrections due to clock size and particle creation coefficients, are observable. These findings may serve as a guideline when performing experiments on simulation of moving cavities in superconducting circuits

Öppna och slutna frågor i en jämförande studie : En studie i hur arbete med öppna/slutna frågor påverkar elevers förmåga till perspektivbyte i tid och rum.

Vi har i vår forskning belyst hur elever upplever arbetet med öppna respektive slutna frågor. Vi har framförallt tittat på hur arbetet med öppna och slutna frågor haft för inverkan på elevers möjligheter till perspektivbyte i tid och rum. Öppna frågor har i vår forskning varit lika med hög frihetsgrad medan slutna frågor är lika med låg eller ingen frihetsgrad. Vi har i vår forskning jämfört resultatet av en essäuppgift från två grupper med elever från årskurs 6. Dessa två grupper har innan uppgiften vägletts i temat ”En resa till Kina” i var sin experimentlektion. Den ena gruppen genomförde en lektion med uteslutande slutna frågor medan den andra gruppen utförde en lektion med uteslutande öppna frågor. En av oss agerade lärare medan övriga två observerade både lärare och elever under experimentlektionerna. För att vi skulle ha en sådan objektiv syn på resultatet som forskningen kräver så valde vi att anonymisera eleverna genom att ge dem nummer i stället för namn. Dessa nummer kunde efter bedömningen av uppgiften härledas till en lista med namn och nummer som deras mentor iordningställt. Vi har även använt oss av enkäter för att ta reda på hur eleverna upplevde arbetet med öppna respektive slutna frågor. Vi har genom vår forskning kommit fram till att elevers möjlighet till perspektivbyte i tid och rum underlättas med hjälp av frihetsgraden på de frågor som används i undervisningen. Vi har visat på att de frågor som har en viss till stor frihetsgrad är de frågor som legat till grund för perspektivbyte i elevernas essäskrivningar. Det är även dessa frågor från experimentlektionerna som eleverna i sina essäskrivningar visar att de minns. Resultatet av enkäten visar att eleverna ställer sig positiva till de arbetssätt som bedrevs under deras experimentlektioner. We have in our research looked at how students experience work with open and closed questions. We have mainly looked at how work with open and closed questions affect student’s possibilities to change perspective in time and space. Open questions have in our research been equal to high freedom degree while closed questions is equal to low or none freedom degree. We have in our research compared the results of an essay task from two group’s with students from grade 6. These two groups had before the task been guided in the theme “A journey to China” in two separate experiment lessons. One group had a lesson with exclusively closed questions and the other group had a lesson with exclusively open questions. One of us acted as a teacher while the other two acted as observers, and observed both the teacher and the students during the experiment lesson. To be able to have an objective view of the result as the research demands we chose to anonymous the students and give them a number instead of names. These number could later on be deduced to a list with name and numbers that there mentor had set up. We have also used questionnaire to be able to see what the students thought of the work with open and closed questions. We have through our research been able to see that student’s possibilities to make a change in perspective in time and space make easy if the freedom degree of the questions used in their lessons. We have showed that the questions that have some or a great deal of freedom degree is the questions that are the foundation of the change of perspective in the students essay tasks. It’s also these questions from the experiment lessons that the students in their essay task show what they remembers. The result from the questionnaire shows that the students are positive to the work method that was carried out during their experiment lessons