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Wolfgang P. Schleich

Publications and source records attributed to Wolfgang P. Schleich.

At least 19 recordsLinked to original sources

Trap-Quenched Matter-Wave Optics in Space

Dual-species atomic sources in space promise to be the testbed for a multitude of searches in quantum gas physics such as a precise test of the Universality of Free Fall (UFF), few-body physics, cold molecules and quantum bubbles. These experiments demand exquisite control over the expansion energies of both condensed ensembles as well as over their differential center-of-mass dynamics. We propose a trap-quenched collimation technique featuring in-trap excitations of collective modes compatible with state-of-the-art atom-chip setups. Using NASA's Cold Atom Laboratory aboard the International Space Station, we demonstrate it on a single-species $^{87}$Rb condensate. By controlling the center-of-mass release dynamics, we observe free expansion times up to 700 ms and measure a two-dimensional expansion energy of $k_B \cdot 78\pm 9 \;\mathrm{pK}$ in the imaging plane. A detailed model of the magnetically-induced dynamics indicates that this corresponds to a two-dimensional expansion energy of about $k_B \cdot 15^{+12}_{-5}\; \mathrm{pK}$ along two of the condensate's eigenaxes. Finally, we theoretically study this trap-quenched collimation scheme for a $^{41}$K-$^{87}$Rb mixture, predicting a simultaneous collimation that meets the expansion energy requirements for a state-of-the-art UFF test at the $10^{-15}$ accuracy level.

physics.atom-ph↗

Observation of Phase Space Dynamics of Inverted Harmonic Oscillator

We have experimentally realized a parabolic potential barrier for surface gravity water waves. The analogy between the resulting wave equation and the Schrodinger equation for the inverted harmonic oscillator (IHO) enables us to study the propagation of quantum-mechanical wave packets with different average energies in this iconic scattering model. We observe a clear boundary in the phase-space dynamics, namely the separatrix, which distinguishes wave packets with energies below the maximum of the IHO potential from those with energies above it. In the former case, the wave packet is blocked, whereas in the latter case, it is transmitted. We also measure the corresponding variation in momentum during this process.

physics.class-ph↗

A logarithmic phase singularity at the heart of Landau-Zener transitions

Three ingredients of the elementary Landau-Zener problem determine the familiar expression $a_{LZ}\equiv\exp\left[-π/(2ε)\right]$ for the asymptotic value of the probability amplitude for remaining in the initial level: (i) A wave whose phase is determined by the product of a contour integral over a simple pole at the origin of the complex plane and the inverse of twice the scaled chirp parameter $ε$. (ii) An asymptotic limit of the associated path connecting the points $\pm 1$ along the real axis and circumventing the pole in the upper half-plane, and (iii) a half-circle in the lower half plane enclosing together with the asymptotic path the pole. The Cauchy theorem immediately provides us with the value $\iiπ$ of the asymptotic contour, and thus with $a_{LZ}$. Our analysis demonstrates not only that $a_{LZ}$ is the consequence of a logarithmic phase singularity but also explains why the Markov approximation also leads to $a_{LZ}$.

quant-ph↗

Elementary asymptotic approach to the Landau-Zener problem

We present an asymptotic approach towards the standard Landau-Zener problem based on two linearly independent elementary waves of constant amplitude but time-dependent phase. The two contributions to this phase are quadratic and logarithmic in time and result from the linear chirp of the energies and the lowest order correction in the coupling between the two levels in the long-time limit. Indeed, our solutions subjected to initial conditions at a large but finite time in the past, are valid for large negative and large positive times. Due to their asymptotic nature they are not valid in the neighborhood of the moment when the levels cross. However, as the starting point of the dynamics moves further into the past, the time interval of the break-down of our asymptotic solutions shrinks and vanishes in the limit of the infinite past which corresponds to the standard Landau-Zener situation. Our approach explains not only every feature of the exact solution but yields deeper insights into the origin of the effects. In particular, it (i) brings to light the subtleties involved in the asymptotic limit leading to the standard expressions for the Landau-Zener transition amplitudes, (ii) identifies the logarithmic phase as the origin of the exponential transition probability amplitude, and (iii) reveals the structure of the lowest order corrections to the Landau-Zener result when the starting point is not in the infinite past.

quant-ph↗

Time-reversal Interferometry Using Cat States with Scalable Entangling Resources

We propose a novel method for generating Schrödinger-cat states -- defined as equal superpositions of arbitrary coherent states -- using a concise sequence of rapid twist-and-turn pulses. We demonstrate that the required shearing strength for the protocol, which scales linearly with time, decreases with increasing number of atoms ($N$) in proportion to $1/\sqrt{N}$. The resulting states exhibit optimal quantum Fisher information, making them ideal for surpassing the classical limit of phase sensitivity in quantum metrology applications. Notably, our protocol is compatible with a time-reversal strategy for quantum metrology, ensuring its practical viability. Furthermore, we demonstrate that the Heisenberg limit scaling remains intact even when reducing the twisting employed in tandem with the number of atoms, thereby mitigating realistic losses such as photon scattering.

quant-ph↗

Advanced Quantum Communication and Quantum Networks -- From basic research to future applications

Classical communication is the basis for many of our current and future technologies, such as mobile phones, video conferences, autonomous vehicles and particularly the internet. In contrast, quantum communication is governed by the laws of quantum mechanics. Due to this fundamental difference, it might offer enormous benefits for security applications, more precise measurements, faster computations, and many other fields of application by interconnecting different quantum devices, such as quantum sensors, quantum computers, or quantum memories. This review provides an overview of the specific properties of quantum information networks. This includes the interfaces between the classical and the quantum regime, the transmission of the quantum information by physical implementations, and potential future applications of quantum networks. We aim to provide a starting point based on fundamental concepts of quantum information processing for further research on a future quantum internet.

quant-ph↗

Observation of quantum free fall and the consistency with the equivalence principle

The unification of quantum theory and the general theory of relativity - describing gravity, is one of the most important challenges in science. Einstein's general theory of relativity is based on the principle of equivalence, and has been confirmed to great accuracy for large bodies. However, in the quantum domain the equivalence principle has been predicted to take a unique form involving a gauge phase, equal to the quantum phase of a free-falling object. To measure this phase, we realize a novel cold-atom interferometer in which one wave-packet stays static in the laboratory frame while the other is in free fall. The observed relative-phase of the wave-packets confirms the predicted phase of a free-falling object, and shows that in our low energy regime, the equivalence principle may be applied to the quantum domain. Our observation constitutes a fundamental test of the interface between quantum theory and gravity. The new interferometer also opens the door for further probing of the latter interface, as well as to searches for new physics.

quant-ph↗

Space magnetometry with a differential atom interferometer

Atom interferometers deployed in space are excellent tools for high precision measurements, navigation, or Earth observation. In particular, differential interferometric setups feature common-mode noise suppression and enable reliable measurements in the presence of ambient platform noise. Here we report on orbital magnetometry campaigns performed with differential single- and double-loop interferometers in NASA's Cold Atom Lab aboard the International Space Station. By comparing measurements with atoms in magnetically sensitive and insensitive states, we have realized atomic magnetometers mapping magnetic field curvatures. Our results pave the way towards precision quantum sensing missions in space.

physics.atom-ph↗

Hidden facts in Landau-Zener transitions revealed by the Riccati Equation

We express the dynamics of the two probability amplitudes in the elementary Landau-Zener problem in terms of the solution of the corresponding Riccati differential equation and identify three key features: (i) The solution of the Riccati equation provides the bridge between the two probability amplitudes. (ii) Neglecting the non-linearity in the Riccati equation is equivalent to the Markov approximation which yields the exact asymptotic expression for one of the probability amplitudes, and (iii) the Riccati equation identifies the origin of the failure of the Markov approximation not being able to provide us in general with the correct asymptotic expression of the other probability amplitude. Our approach relies on approximate yet analytical solutions of the Riccati equation in different time regimes, highlighting the impact of its non-linear nature on the time evolution of the system.

quant-ph↗

Conformal duality of the nonlinear Schrödinger equation: Theory and applications to parameter estimation

The nonlinear Schrödinger equation (NLSE) is a rich and versatile model, which in one spatial dimension has stationary solutions similar to those of the linear Schrödinger equation as well as more exotic solutions such as solitary waves and quantum droplets. Here we present the unified theory of the NLSE, showing that all stationary solutions of the local one-dimensional cubic-quintic NLSE can be classified according to a single number called the cross-ratio. Any two solutions with the same cross-ratio can be converted into one another using a conformal transformation, and the same also holds true for traveling wave solutions. Further, we introduce an optimization afterburner that relies on this conformal symmetry to substantially improve NLSE parameter estimation from noisy empirical data. The new method therefore should have far reaching practical applications for nonlinear physical systems.

cond-mat.quant-gas↗

Optimal Diffractive Focusing of Quantum Waves

Following the familiar analogy between the optical paraxial wave equation and the Schrödinger equation, we derive the optimal, real-valued wave function for focusing in one and two space dimensions without the use of any phase component. We compare and contrast the focusing parameters of the optimal waves with those of other diffractive focusing approaches, such as Fresnel zones. Moreover, we experimentally demonstrate these focusing properties on optical beams using both reflective and transmissive liquid crystal devices. Our results provide an alternative direction for focusing waves where phase elements are challenging to implement, such as for X-rays, THz radiation, and electron beams.

physics.optics↗

A different perspective on the Landau-Zener dynamics

We present two different approaches towards the Landau-Zener problem: (i) The Markov approximation in the integro-differential equation for one of the two probability amplitudes, and (ii) an amplitude-and-phase analysis of the linear second order differential equation for same probability amplitude. Our treatment shows that the Markov approximation neglects the non-linearity of the equation but still provides us with the exact asymptotic result.

quant-ph↗

Interferometry of Atomic Matter Waves in the Cold Atom Lab onboard the International Space Station

Ultracold atomic gases hold unique promise for space science by capitalizing on quantum advantages and extended freefall, afforded in a microgravity environment, to enable next-generation precision sensors. Atom interferometers are a class of quantum sensors which can use freely falling gases of atoms cooled to sub-photon-recoil temperatures to provide unprecedented sensitivities to accelerations, rotations, and gravitational forces, and are currently being developed for space-based applications in gravitational, earth, and planetary sciences, as well as to search for subtle forces that could signify physics beyond General Relativity and the Standard Model. NASA's Cold Atom Lab (CAL) operates onboard the International Space Station as a multi-user facility for studies of ultracold atoms and to mature quantum technologies, including atom interferometry, in persistent microgravity. In this paper, we report on path-finding experiments utilizing ultracold $^{87}$Rb atoms in the CAL atom interferometer, which was enabled by an on-orbit upgrade of the CAL science module: A three-pulse Mach-Zehnder interferometer was studied to understand limitations from the influence of ISS vibrations. Additionally, Ramsey shear-wave interferometry was used to manifest interference patterns in a single run that were observable for over 150 ms free-expansion time. Finally, the CAL atom interferometer was used to remotely measure the photon recoil from the atom interferometer laser as a demonstration of the first quantum sensor using matter-wave interferometry in space.

physics.atom-ph↗

Atom interferometry with quantized light pulses

The far-field patterns of atoms diffracted from a classical light field, or from a quantum one in a photon-number state are identical. On the other hand, diffraction from a field in a coherent state, which shares many properties with classical light, displays a completely different behavior. We show that in contrast to the diffraction patterns, the interference signal of an atom interferometer with light-pulse beam splitters and mirrors in intense coherent states does approach the limit of classical fields. However, low photon numbers reveal the granular structure of light, leading to a reduced visibility since Welcher-Weg (which-way) information is encoded into the field. We discuss this effect for a single photon-number state as well as a superposition of two such states.

quant-ph↗

Quantum Gas Mixtures and Dual-Species Atom Interferometry in Space

The capability to reach ultracold atomic temperatures in compact instruments has recently been extended into space. Ultracold temperatures amplify quantum effects, while free-fall allows further cooling and longer interactions time with gravity - the final force without a quantum description. On Earth, these devices have produced macroscopic quantum phenomena such as Bose-Einstein condensation (BECs), superfluidity, and strongly interacting quantum gases. Quantum sensors interfering the superposition of two ultracold atomic isotopes have tested the Universality of Free Fall (UFF), a core tenet of Einstein's classical gravitational theory, at the $10^{-12}$ level. In space, cooling the elements needed to explore the rich physics of strong interactions and preparing the multiple species required for quantum tests of the UFF has remained elusive. Here, utilizing upgraded capabilities of the multi-user Cold Atom Lab (CAL) instrument within the International Space Station (ISS), we report the first simultaneous production of a dual species Bose-Einstein condensate in space (formed from $^{87}$Rb and $^{41}$K), observation of interspecies interactions, as well as the production of $^{39}$K ultracold gases. We have further achieved the first space-borne demonstration of simultaneous atom interferometry with two atomic species ($^{87}$Rb and $^{41}$K). These results are an important step towards quantum tests of UFF in space, and will allow scientists to investigate aspects of few-body physics, quantum chemistry, and fundamental physics in novel regimes without the perturbing asymmetry of gravity.

cond-mat.quant-gas↗

Interference of Clocks: A Quantum Twin Paradox

The phase of matter waves depends on proper time and is therefore susceptible to special-relativistic (kinematic) and gravitational (redshift) time dilation. Hence, it is conceivable that atom interferometers measure general-relativistic time-dilation effects. In contrast to this intuition, we show: (i.) Closed light-pulse interferometers without clock transitions during the pulse sequence are not sensitive to gravitational time dilation in a linear potential. (ii.) They can constitute a quantum version of the special-relativistic twin paradox. (iii.) Our proposed experimental geometry for a quantum-clock interferometer isolates this effect.

quant-ph↗

The Wave Functional of the Vacuum in a Resonator

We show that despite the fundamentally different situations, the wave functional of the vacuum in a resonator is identical to that of free space. The infinite product of Gaussian ground state wave functions defining the wave functional of the vacuum translates into an exponential of a sum rather than an integral over the squares of mode amplitudes weighted by the mode volume and a power of the mode wave number. We express this sum by an integral of a bilinear form of the field containing a kernel given by a function of the square root of the negative Laplacian acting on a transverse delta function. For transverse fields it suffices to employ the familiar delta function which allows us to obtain explicit expressions for the kernels of the vector potential, the electric field and the magnetic induction. We show for the example of the vector potential that different mode expansions lead to different kernels. Lastly, we show that the kernels have a close relationship with the Wightman correlation functions of the fields.

physics.gen-ph↗