There is no need to store summer heat for the entire winter, which would necessitate a far larger capacity system.
One would only need to store solar thermal energy that is available on any sunny or partly sunny day for night time and cloudy days.
Where I live about half of all days produce abundant solar thermal energy even in the depth of winter. Calculating in night time, you end up with about 12.5% of total winter time having abundant free thermal energy.
So one would need to build a system of solar thermal collectors about 8 times the size one would need to heat a house on a sunny winter day, and that is not a very big system.
Space wise I think it would work for single family residential homes on .25 acre lots if the house was designed for it from the start.
This exists already and is called a liquid to water heat pump, where a liquid is circulated in long pipes either buried under your lawn (if it's big enough) or inserted in holes drilled several hundred feet deep, and then passed through a heat pump to provide hot water that's then distributed through your house.
You just need to go ~20 ft down for the thermal mass of the soil to significantly damp out even annual oscillations, so there the soil temperature equals the mean temperature where you live.
The main barrier to adaptation is that most people don't have a big enough lawn for the shallow method, and the cost of the deep method is big enough that it takes too long to break-even for most people.
What we really need for any such method to succeed is that governments must make it mandatory for new houses, then we can get economies of scale and probably make it viable also for retrofits.
Heat pumps have greater than 100 percent efficiency when compared to a regular resistive electric heater (which is already 100 percent efficient, when measured as heat out / energy in).
Everyone always forgets about the part where you're cooling down the outside...
Yes. Heat-pumps will make up for some losses from all other steps but I highly doubt it all togrther will reach efficiency of purely thermal system. Heat pumps also rely on access to medium that they cool down to get the additional heat and are at least as complex as a fridge or air conditioner.
It might be that one or the other is better "in general", but I can see that this technology could have benefits in certain scenarios, maybe long term storage in remote, cold climates.
No current electric battery technology has the energy density to heat a house all winter economically. You'd need a volume of batteries similar to the volume of your house.
One would only need to store solar thermal energy that is available on any sunny or partly sunny day for night time and cloudy days.
Where I live about half of all days produce abundant solar thermal energy even in the depth of winter. Calculating in night time, you end up with about 12.5% of total winter time having abundant free thermal energy.
So one would need to build a system of solar thermal collectors about 8 times the size one would need to heat a house on a sunny winter day, and that is not a very big system.
Space wise I think it would work for single family residential homes on .25 acre lots if the house was designed for it from the start.