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Two-photon E1-M1 clock transition excitation in 174Yb atoms for quantum clock interferometry

Mario Antonio Montero Sanchez, Ali Lezeik, Koester, Dominik, Klaus Zipfel, Christian Schubert, Ernst Maria Rasel, Dennis Schlippert

Published Sep 1, 2024• 0 citations
OpenAlex

Abstract

Atom interferometers are excellent tools for measuring inertial forces. Their high accuracy and sensitivity allow them to test fundamental physics, e.g., Einstein’s equivalence principle (EEP). One of the main assumptions of EEP is the universality of gravitational redshift (UGR), which states that the ticking rate measured by two idealised clocks at different points in a gravitational field is independent of their internal composition [1]. Although UGR has been successfully tested with two independent atomic clocks, the same effect on a single clock in a delocalised superposition of states has not been observed yet [2]. A promising approach for a delocalised test of UGR is quantum clock interferometry (QCI), which uses a sequence of light pulses to split, redirect, and recombine coherent wave packets and drive transitions between the internal states of the atoms to measure differences in proper time imprinted in the interferometer’s phase shift [3]. An experimental realisation of such schemes requires atomic species with large internal transitions. In this work, we propose an interferometry sensitive to gravitational redshift. By performing a double differential measurement in a single shot, this configuration benefits from a common-mode rejection of spurious effects in the interferometer’s phase. The feasibility of QCI experiments measuring gravitational redshift depends on the availability of long-lived internal states with large energy differences, making the ytterbium (Yb) optical transition an ideal candidate. The clock transition is excited through a two-photon Doppler-free E1-M1 mechanism [4]. This process requires a narrow linewidth, 1 kHz, and a high-power, 20 W, light source. We present our frequency stabilisation scheme and power amplification of an 1156 nm laser to drive the clock transition on a cold Yb cloud. [1] F. Di Pumpo et al., Phys. Rev. D 107, 064007 (2023). [2] A. Roura et al., Phys. Rev. D 104 084001 (2021). [3] C. Ufrecht et al., Phys. Rev. Research 2 043240 (2020). [4] E. A. Alden et al., Phys. Rev. A 90, 012523 (2014)

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Towards a two-photon E1-M1 clock transition excitation in ^{174}Yb for quantum clock interferometry

Montero Sanchez, Mario Antonio, Lezeik, Ali, Koester, Dominik +4 more

Atom interferometry experiments measuring gravitational redshift require access to long-lived internal states, such as the 1S0-3P0 optical transition in group II atoms. An E1-M1 two-photon excitation directly access the clock state from the ground state by coupling to a far detuned intermediate state through a pair of electric and magnetic dipole allowed transitions [1]. This avoids state mixing, enhancing the excited state’s lifetime. Moreover, using counter-propagating photons with degenerate frequencies eliminates first-order Doppler effects. We report the progress of our experimental setup to drive the clock transition. We prepare an ultra-cold atomic ensemble of 174Yb through a dual-stage magneto-optical trap sequence, followed by evaporative cooling in a crossed optical dipole trap [2]. To excite the transition, we utilize a high power (10 W), narrow-linewidth l1156 nm laser system referenced to a high-finesse cavity and a frequency comb. We discuss further applications of the two-photon Doppler-free excitation as a beam splliting method for quantum clock interferometry experiments. [1]PRA 90, 012523 (2014). [2]J.Phys.B 54, 035302 (2021)

•Mar 11, 2025•0 citations

Gravitational Redshift in Quantum-Clock Interferometry

Albert Roura

The creation of delocalized coherent superpositions of quantum systems experiencing different relativistic effects is an important milestone in future research at the interface of gravity and quantum mechanics.This milestone could be achieved by generating a superposition of quantum clocks that follow paths with different gravitational time dilation and investigating the consequences on the interference signal when they are eventually recombined.Light-pulse atom interferometry with elements employed in optical atomic clocks is a promising candidate for that purpose, but it suffers from major challenges including its insensitivity to the gravitational redshift in a uniform field.All of these difficulties can be overcome with the novel scheme presented here, which is based on initializing the clock when the spatially separate superposition has already been generated and performing a doubly differential measurement where the differential phase shift between the two internal states is compared for different initialization times.This scheme can be exploited to test the universality of the gravitational redshift with delocalized coherent superpositions of quantum clocks, and it is argued that its experimental implementation should be feasible with a new generation of 10-meter atomic fountains that will soon become available.Interestingly, the approach also offers significant advantages for more compact setups based on guided interferometry or hybrid configurations.Furthermore, in order to provide a solid foundation for the analysis of the various interferometry schemes and the effects that can be measured with them, a general formalism for a relativistic description of atom interferometry in curved spacetime is developed.It can describe freely falling atoms as well as the effects of external forces and guiding potentials, and it can be applied to a very wide range of situations.As an important ingredient for quantum-clock interferometry, suitable diffraction mechanisms for atoms in internal-state superpositions are investigated too.Finally, the relation of the proposed doubly differential measurement scheme to other experimental approaches and to tests of the universality of free fall is discussed in detail.

arXiv:1810.06744•Physical Review X•Apr 20, 2020•80 citations

Gravitational redshift in quantum-clock interferometry

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The creation of delocalized coherent superpositions of quantum systems experiencing di erent relativistic e ects is an important milestone in future research at the interface of gravity and quantum mechanics. This could be achieved by generating a superposition of quantum clocks that follow paths with di erent gravitational time dilation and investigating the consequences on the interference signal when they are eventually recombined. Light-pulse atom interferometry with elements employed in optical atomic clocks is a promising candidate for that purpose, but su ers from major challenges including its insensitivity to the gravitational redshift in a uniform eld. All these di- culties can be overcome with a novel scheme presented here which is based on initializing the clock when the spatially separate superposition has already been generated and performing a doubly differential measurement where the di erential phase shift between the two internal states is compared for di erent initialization times. This can be exploited to test the universality of the gravitational redshift (UGR) with delocalized coherent superpositions of quantum clocks and it is argued that its experimental implementation should be feasible with a new generation of 10-meter atomic fountains that will soon become available. Interestingly, the approach also o ers signi cant advantages for more compact set-ups based on guided interferometry or hybrid con gurations. Furthermore, in order to provide a solid foundation for the analysis of the various interferometry schemes and the e ects that can be measured with them, a general formalism for a relativistic description of atom interferometry in curved spacetime is developed. It can deal with freely falling atoms, but also include the e ects of external forces and guiding potentials, and can be applied to a very wide range of situations. As an important ingredient for quantum-clock interferometry, suitable difraction mechanisms for atoms in internal-state superpositions are investigated too. Finally, the relation of the proposed doubly-di erential measurement scheme to other experimental approaches and to tests of the universality of free fall (UFF) is discussed in detail.

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Measuring gravitational time dilation with delocalized quantum superpositions

Albert Roura, Christian Schubert, Dennis Schlippert +1 more

Atomic clocks can measure the gravitational redshift predicted by general relativity with great accuracy and for height differences as little as 1 cm. All existing experiments, however, involve the comparison of two independent clocks at different locations rather than a single clock in a delocalized quantum superposition. Here we present an interferometry scheme employing group-II-type atoms, such as Sr or Yb, capable of measuring the gravitational time dilation in a coherent superposition of atomic wave packets at two different heights. In contrast to other recent proposals, there is no need for pulses that can efficiently diffract both internal states. Instead, the scheme relies on very simple atom optics for which high diffraction efficiencies can be achieved with rather mild requirements on laser power. Furthermore, the effects of vibration noise are subtracted by employing a simultaneous Rb interferometer that acts as an inertial reference. Remarkably, the recently commissioned VLBAI facility in Hannover, a 10-m atomic fountain that can simultaneously operate Yb and Rb atoms and enables up to 2.8 s of free evolution time, meets all the requirements for a successful experimental implementation.

arXiv:2010.11156•Physical review. D/Physical review. D.•Oct 1, 2021•35 citations

Atom interferometry for tests of general relativity

Loriani Fard

The search for a fundamental, self-consistent theoretical framework to cover phenomena over all energy scales is possibly the most challenging quest of contemporary physics. Approaches to reconcile quantum mechanics and general relativity entail the modification of their foundations such as the equivalence principle. This corner stone of general relativity is suspected to be violated in various scenarios and is therefore under close scrutiny. Experiments based on the manipulation of cold atoms are excellently suited to challenge its different facets. Freely falling atoms constitute ideal test masses for tests of the universality of free fall in interferometric setups. Moreover, the superposition of internal energy eigenstates provides the notion of a clock, which allows to perform tests of the gravitational redshift. Furthermore, as atom interferometers constitute outstanding phasemeters, they hold the promise to detect gravitational waves, another integral aspect of general relativity. In recent years, atom interferometers have developed into versatile sensors with excellent accuracy and stability, and allow to probe physics at the interface of quantum mechanics and general relativity without classical analog. In this thesis, various aspects regarding tests of general relativity with atom interferometry have been theoretically investigated. This includes the analysis of fundamental effects as well as feasibility studies of experimental configurations. The work is partially focussed on a space-borne mission scenario for a dedicated quantum test of the universality of free fall beyond state-of-the-art by dropping matter waves of different elements. To enable the target accuracy at the level of 10^(−17), a compensation scheme has been developed and discussed, mitigating the detrimental effects of imperfect test mass co-location upon release and relaxing the requirements on the source preparation by several orders of magnitude. In addition, it was demonstrated that the careful design of quantum degenerate sources is indispensable for these experiments, requiring tailored schemes to prepare miscible binary sources. The possibility to test the gravitational redshift with atom interferometers has also been examined in this thesis and connected to the ideas of clock interferometry. With the proof that closed light pulse atom interferometers without transitions between internal internal states are not sensitive to gravitational time dilation, an ongoing scientific debate has been resolved. Instead, certain configurations were shown to implement a quantum version of the special-relativistic twin paradox, for which an experiment has been proposed. Finally, requirements on atomic sources and atom optics for scenarios of gravitational wave detection on ground and in space have been investigated.

•Jan 1, 2020•0 citations

Gravitational redshift in quantum-clock interferometry

Albert Roura

Remarkable advances in atom interferometry have enabled the creation of macroscopically delocalized quantum superpositions with atomic wave packets separated up to half a meter. Nevertheless, in all cases realized so far the differences in the dynamics of the two wave packets of the superposition can be entirely described in terms of Newtonian mechanics. Therefore, the creation of delocalized coherent superpositions of quantum systems experiencing different relativistic effects is an important milestone in future research at the interface of gravity and quantum mechanics. This could be achieved by generating a superposition of quantum clocks that follow paths with different gravitational time dilation and investigating the consequences on the interference signal when they are eventually recombined. After explaining the major challenges that quantum-clock interferometry based on light-pulse atom interferometers is confronted with (including their insensitivity to gravitational redshift in a uniform field), I will present a promising scheme capable of measuring the effects of gravitational time dilation in interfering quantum clocks. Its experimental implementation should be within reach of the 10-meter atomic fountains of Sr and Yb atoms that will soon become available in Stanford and HITec (Hanover) respectively.

•Jan 1, 2021•72 citations
Atom interferometers are excellent tools for measuring inertial forces. Their high accuracy and sensitivity allow them to test fundamental physics, e.g., Einstein’s equivalence principle (EEP). One of the main assumptions of EEP is the universality of gravitational redshift (UGR), which states that the ticking rate measured by two idealised clocks at different points in a gravitational field is independent of their internal composition [1]. Although UGR has been successfully tested with two independent atomic clocks, the same effect on a single clock in a delocalised superposition of states has not been observed yet [2]. A promising approach for a delocalised test of UGR is quantum clock interferometry (QCI), which uses a sequence of light pulses to split, redirect, and recombine coherent wave packets and drive transitions between the internal states of the atoms to measure differences in proper time imprinted in the interferometer’s phase shift [3]. An experimental realisation of such schemes requires atomic species with large internal transitions. In this work, we propose an interferometry sensitive to gravitational redshift. By performing a double differential measurement in a single shot, this configuration benefits from a common-mode rejection of spurious effects in the interferometer’s phase. The feasibility of QCI experiments measuring gravitational redshift depends on the availability of long-lived internal states with large energy differences, making the ytterbium (Yb) optical transition an ideal candidate. The clock transition is excited through a two-photon Doppler-free E1-M1 mechanism [4]. This process requires a narrow linewidth, 1 kHz, and a high-power, 20 W, light source. We present our frequency stabilisation scheme and power amplification of an 1156 nm laser to drive the clock transition on a cold Yb cloud. [1] F. Di Pumpo et al., Phys. Rev. D 107, 064007 (2023). [2] A. Roura et al., Phys. Rev. D 104 084001 (2021). [3] C. Ufrecht et al., Phys. Rev. Research 2 043240 (2020). [4] E. A. Alden et al., Phys. Rev. A 90, 012523 (2014)
Atom interferometry experiments measuring gravitational redshift require access to long-lived internal states, such as the 1S0-3P0 optical transition in group II atoms. An E1-M1 two-photon excitation directly access the clock state from the ground state by coupling to a far detuned intermediate state through a pair of electric and magnetic dipole allowed transitions [1]. This avoids state mixing, enhancing the excited state’s lifetime. Moreover, using counter-propagating photons with degenerate frequencies eliminates first-order Doppler effects. We report the progress of our experimental setup to drive the clock transition. We prepare an ultra-cold atomic ensemble of 174Yb through a dual-stage magneto-optical trap sequence, followed by evaporative cooling in a crossed optical dipole trap [2]. To excite the transition, we utilize a high power (10 W), narrow-linewidth l1156 nm laser system referenced to a high-finesse cavity and a frequency comb. We discuss further applications of the two-photon Doppler-free excitation as a beam splliting method for quantum clock interferometry experiments. [1]PRA 90, 012523 (2014). [2]J.Phys.B 54, 035302 (2021)
The creation of delocalized coherent superpositions of quantum systems experiencing different relativistic effects is an important milestone in future research at the interface of gravity and quantum mechanics.This milestone could be achieved by generating a superposition of quantum clocks that follow paths with different gravitational time dilation and investigating the consequences on the interference signal when they are eventually recombined.Light-pulse atom interferometry with elements employed in optical atomic clocks is a promising candidate for that purpose, but it suffers from major challenges including its insensitivity to the gravitational redshift in a uniform field.All of these difficulties can be overcome with the novel scheme presented here, which is based on initializing the clock when the spatially separate superposition has already been generated and performing a doubly differential measurement where the differential phase shift between the two internal states is compared for different initialization times.This scheme can be exploited to test the universality of the gravitational redshift with delocalized coherent superpositions of quantum clocks, and it is argued that its experimental implementation should be feasible with a new generation of 10-meter atomic fountains that will soon become available.Interestingly, the approach also offers significant advantages for more compact setups based on guided interferometry or hybrid configurations.Furthermore, in order to provide a solid foundation for the analysis of the various interferometry schemes and the effects that can be measured with them, a general formalism for a relativistic description of atom interferometry in curved spacetime is developed.It can describe freely falling atoms as well as the effects of external forces and guiding potentials, and it can be applied to a very wide range of situations.As an important ingredient for quantum-clock interferometry, suitable diffraction mechanisms for atoms in internal-state superpositions are investigated too.Finally, the relation of the proposed doubly differential measurement scheme to other experimental approaches and to tests of the universality of free fall is discussed in detail.
The creation of delocalized coherent superpositions of quantum systems experiencing di erent relativistic e ects is an important milestone in future research at the interface of gravity and quantum mechanics. This could be achieved by generating a superposition of quantum clocks that follow paths with di erent gravitational time dilation and investigating the consequences on the interference signal when they are eventually recombined. Light-pulse atom interferometry with elements employed in optical atomic clocks is a promising candidate for that purpose, but su ers from major challenges including its insensitivity to the gravitational redshift in a uniform eld. All these di- culties can be overcome with a novel scheme presented here which is based on initializing the clock when the spatially separate superposition has already been generated and performing a doubly differential measurement where the di erential phase shift between the two internal states is compared for di erent initialization times. This can be exploited to test the universality of the gravitational redshift (UGR) with delocalized coherent superpositions of quantum clocks and it is argued that its experimental implementation should be feasible with a new generation of 10-meter atomic fountains that will soon become available. Interestingly, the approach also o ers signi cant advantages for more compact set-ups based on guided interferometry or hybrid con gurations. Furthermore, in order to provide a solid foundation for the analysis of the various interferometry schemes and the e ects that can be measured with them, a general formalism for a relativistic description of atom interferometry in curved spacetime is developed. It can deal with freely falling atoms, but also include the e ects of external forces and guiding potentials, and can be applied to a very wide range of situations. As an important ingredient for quantum-clock interferometry, suitable difraction mechanisms for atoms in internal-state superpositions are investigated too. Finally, the relation of the proposed doubly-di erential measurement scheme to other experimental approaches and to tests of the universality of free fall (UFF) is discussed in detail.
Atomic clocks can measure the gravitational redshift predicted by general relativity with great accuracy and for height differences as little as 1 cm. All existing experiments, however, involve the comparison of two independent clocks at different locations rather than a single clock in a delocalized quantum superposition. Here we present an interferometry scheme employing group-II-type atoms, such as Sr or Yb, capable of measuring the gravitational time dilation in a coherent superposition of atomic wave packets at two different heights. In contrast to other recent proposals, there is no need for pulses that can efficiently diffract both internal states. Instead, the scheme relies on very simple atom optics for which high diffraction efficiencies can be achieved with rather mild requirements on laser power. Furthermore, the effects of vibration noise are subtracted by employing a simultaneous Rb interferometer that acts as an inertial reference. Remarkably, the recently commissioned VLBAI facility in Hannover, a 10-m atomic fountain that can simultaneously operate Yb and Rb atoms and enables up to 2.8 s of free evolution time, meets all the requirements for a successful experimental implementation.
The search for a fundamental, self-consistent theoretical framework to cover phenomena over all energy scales is possibly the most challenging quest of contemporary physics. Approaches to reconcile quantum mechanics and general relativity entail the modification of their foundations such as the equivalence principle. This corner stone of general relativity is suspected to be violated in various scenarios and is therefore under close scrutiny. Experiments based on the manipulation of cold atoms are excellently suited to challenge its different facets. Freely falling atoms constitute ideal test masses for tests of the universality of free fall in interferometric setups. Moreover, the superposition of internal energy eigenstates provides the notion of a clock, which allows to perform tests of the gravitational redshift. Furthermore, as atom interferometers constitute outstanding phasemeters, they hold the promise to detect gravitational waves, another integral aspect of general relativity. In recent years, atom interferometers have developed into versatile sensors with excellent accuracy and stability, and allow to probe physics at the interface of quantum mechanics and general relativity without classical analog. In this thesis, various aspects regarding tests of general relativity with atom interferometry have been theoretically investigated. This includes the analysis of fundamental effects as well as feasibility studies of experimental configurations. The work is partially focussed on a space-borne mission scenario for a dedicated quantum test of the universality of free fall beyond state-of-the-art by dropping matter waves of different elements. To enable the target accuracy at the level of 10^(−17), a compensation scheme has been developed and discussed, mitigating the detrimental effects of imperfect test mass co-location upon release and relaxing the requirements on the source preparation by several orders of magnitude. In addition, it was demonstrated that the careful design of quantum degenerate sources is indispensable for these experiments, requiring tailored schemes to prepare miscible binary sources. The possibility to test the gravitational redshift with atom interferometers has also been examined in this thesis and connected to the ideas of clock interferometry. With the proof that closed light pulse atom interferometers without transitions between internal internal states are not sensitive to gravitational time dilation, an ongoing scientific debate has been resolved. Instead, certain configurations were shown to implement a quantum version of the special-relativistic twin paradox, for which an experiment has been proposed. Finally, requirements on atomic sources and atom optics for scenarios of gravitational wave detection on ground and in space have been investigated.
Remarkable advances in atom interferometry have enabled the creation of macroscopically delocalized quantum superpositions with atomic wave packets separated up to half a meter. Nevertheless, in all cases realized so far the differences in the dynamics of the two wave packets of the superposition can be entirely described in terms of Newtonian mechanics. Therefore, the creation of delocalized coherent superpositions of quantum systems experiencing different relativistic effects is an important milestone in future research at the interface of gravity and quantum mechanics. This could be achieved by generating a superposition of quantum clocks that follow paths with different gravitational time dilation and investigating the consequences on the interference signal when they are eventually recombined. After explaining the major challenges that quantum-clock interferometry based on light-pulse atom interferometers is confronted with (including their insensitivity to gravitational redshift in a uniform field), I will present a promising scheme capable of measuring the effects of gravitational time dilation in interfering quantum clocks. Its experimental implementation should be within reach of the 10-meter atomic fountains of Sr and Yb atoms that will soon become available in Stanford and HITec (Hanover) respectively.